Calculus, Early Transcendentals
9th Edition
ISBN: 9781337613927
Author: Stewart
Publisher: CENGAGE L
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Textbook Question
Chapter 7.2, Problem 4E
Evaluate the
4.
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74. Geometry of implicit differentiation Suppose x and y are related
0. Interpret the solution of this equa-
by the equation F(x, y)
=
tion as the set of points (x, y) that lie on the intersection of the
F(x, y) with the xy-plane (z = 0).
surface
Z
=
a. Make a sketch of a surface and its intersection with the
xy-plane. Give a geometric interpretation of the result that
dy
dx
=
Fx
F
χ
y
b. Explain geometrically what happens at points where F = 0.
y
Example 3.2. Solve the following boundary value problem by ADM
(Adomian decomposition)
method
with the boundary conditions
მი
მი
z-
= 2x²+3
дг Əz
w(x, 0) = x² - 3x,
θω
(x, 0) = i(2x+3).
ay
6. A particle moves according to a law of motion s(t) = t3-12t2 + 36t, where t is measured in seconds and s is in feet.
(a) What is the velocity at time t?
(b) What is the velocity after 3 s?
(c) When is the particle at rest?
(d)
When is the particle moving in the positive direction?
(e) What is the acceleration at time t?
(f) What is the acceleration after 3 s?
Chapter 7 Solutions
Calculus, Early Transcendentals
Ch. 7.1 - Evaluate the integral using integration by parts...Ch. 7.1 - Evaluate the integral using integration by parts...Ch. 7.1 - Evaluate the integral using integration by parts...Ch. 7.1 - Evaluate the integral using integration by parts...Ch. 7.1 - Evaluate the integral. 6. yeydyCh. 7.1 - Evaluate the integral. 7. xsin10xdxCh. 7.1 - Evaluate the integral. 8. (x)cosxdxCh. 7.1 - Evaluate the integral. 9. wlnwdwCh. 7.1 - Evaluate the integral. 10. lnxx2dxCh. 7.1 - Evaluate the integral. 7. (x2+2x)cosxdx
Ch. 7.1 - Evaluate the integral. 8. t2sintdtCh. 7.1 - Evaluate the integral. 9. cos1xdxCh. 7.1 - Evaluate the integral. 10. lnxdxCh. 7.1 - Evaluate the integral. 11. t4lntdtCh. 7.1 - Evaluate the integral. 12. tan12ydyCh. 7.1 - Evaluate the integral. 13. tcsc2tdtCh. 7.1 - Evaluate the integral. 14. xcoshaxdxCh. 7.1 - Evaluate the integral. 15. (lnx)2dxCh. 7.1 - Evaluate the integral. 16. z10zdzCh. 7.1 - Evaluate the integral. 21. e3xcosxdxCh. 7.1 - Evaluate the integral. 22. exsinxdxCh. 7.1 - Evaluate the integral. 17. e2sin3dCh. 7.1 - Evaluate the integral. 18. ecos2dCh. 7.1 - Evaluate the integral. 19. z3ezdzCh. 7.1 - Evaluate the integral. 22. (arcsinx)2dxCh. 7.1 - Evaluate the integral. 27. 1+x2e3xdxCh. 7.1 - Evaluate the integral. 28. 01/2sin3dCh. 7.1 - Evaluate the integral. 29. 01x3xdxCh. 7.1 - Evaluate the integral. 30. 01xex(1+x)2dxCh. 7.1 - Evaluate the integral. 25. 02ysinhydyCh. 7.1 - Evaluate the integral. 26. 12w2lnwdwCh. 7.1 - Evaluate the integral. 27. 15lnRR2dRCh. 7.1 - Evaluate the integral. 28. 02t2sin2tdtCh. 7.1 - Evaluate the integral. 29. 0xsinxcosxdxCh. 7.1 - Evaluate the integral. 30. 13arctan(1/x)dxCh. 7.1 - Evaluate the integral. 31. 15MeMdMCh. 7.1 - Evaluate the integral. 32. 12(lnx)2x3dxCh. 7.1 - Evaluate the integral. 33. 0/3sinxln(cosx)dxCh. 7.1 - Evaluate the integral. 34. 01r34+r2drCh. 7.1 - Evaluate the integral. 41. 0cosxsinhxdxCh. 7.1 - Evaluate the integral. 36. 0tessin(ts)dsCh. 7.1 - First make a substitution and then use integration...Ch. 7.1 - First make a substitution and then use integration...Ch. 7.1 - First make a substitution and then use integration...Ch. 7.1 - First make a substitution and then use integration...Ch. 7.1 - First make a substitution and then use integration...Ch. 7.1 - First make a substitution and then use integration...Ch. 7.1 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.1 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.1 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.1 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.1 - (a) Use the reduction formula in Example 6 to show...Ch. 7.1 - (a) Prove the reduction formula...Ch. 7.1 - (a) Use the reduction formula in Example 6 to show...Ch. 7.1 - Prove that, for even powers of sine,...Ch. 7.1 - Use integration by parts to prove the reduction...Ch. 7.1 - Use integration by parts to prove the reduction...Ch. 7.1 - Use integration by parts to prove the reduction...Ch. 7.1 - Use integration by parts to prove the reduction...Ch. 7.1 - Use Exercise 57 to find (lnx)3dx . 57....Ch. 7.1 - Use Exercise 58 to find x4exdx . 58....Ch. 7.1 - Find the area of the region bounded by the given...Ch. 7.1 - Find the area of the region bounded by the given...Ch. 7.1 - Use a graph to find approximate x-coordinates of...Ch. 7.1 - Use a graph to find approximate x-coordinates of...Ch. 7.1 - Use the method of cylindrical shells to find the...Ch. 7.1 - Use the method of cylindrical shells to find the...Ch. 7.1 - Use the method of cylindrical shells to find the...Ch. 7.1 - Prob. 70ECh. 7.1 - Calculate the volume generated by rotating the...Ch. 7.1 - Calculate the average value of f(x) = x sec2x on...Ch. 7.1 - The Fresnel function S(x)=0xsin(12t2)dt was...Ch. 7.1 - A Rocket Equation A rocket accelerates by burning...Ch. 7.1 - A particle that moves along a straight line has...Ch. 7.1 - Prob. 76ECh. 7.1 - Suppose that f(l) = 2, f(4) = 7, f(1) = 5, f(4) =...Ch. 7.1 - (a) Use integration by parts to show that...Ch. 7.1 - Prob. 79ECh. 7.1 - We arrived at Formula 6.3.2, V=ab2xf(x)dx, by...Ch. 7.2 - Evaluate the integral. 1. sin3xcos2xdxCh. 7.2 - Evaluate the integral. 2. cos6ysin3ydyCh. 7.2 - Evaluate the integral. 3. 0/2cos9xsin5xdxCh. 7.2 - Evaluate the integral. 4. 0/4sin5xdxCh. 7.2 - Evaluate the integral. 5. sin5(2t)cos2(2t)dtCh. 7.2 - Evaluate the integral. 6. cos3(t/2)sin2(t/2)dtCh. 7.2 - Evaluate the integral. 7. 0/2cos2dCh. 7.2 - Evaluate the integral. 8. 0/4sin2(2)dCh. 7.2 - Evaluate the integral. 9. 0cos4(2t)dtCh. 7.2 - Evaluate the integral. 10. 0sin2tcos4tdtCh. 7.2 - Evaluate the integral. 11. 0/2sin2xcos2xdxCh. 7.2 - Evaluate the integral. 12. 0/2(2sin)2dCh. 7.2 - Evaluate the integral. 13. cossin3dCh. 7.2 - Evaluate the integral. 14. (1+sint3)cos3tdtCh. 7.2 - Evaluate the integral. 15. sinxsec5xdxCh. 7.2 - Evaluate the integral. 16. csc5cos3dCh. 7.2 - Evaluate the integral. 15. cotxcos2xdxCh. 7.2 - Evaluate the integral. 16. tan2xcos3xdxCh. 7.2 - Evaluate the integral. 17. sin2xsin2xdxCh. 7.2 - Evaluate the integral. 18. sinxcos(12x)dxCh. 7.2 - Evaluate the integral. 21. tanxsec3xdxCh. 7.2 - Evaluate the integral. 22. tan2sec4dCh. 7.2 - Evaluate the integral. 23. tan2xdxCh. 7.2 - Evaluate the integral. 24. (tan2x+tan4x)dxCh. 7.2 - Evaluate the integral. 25. tan4xsec6xdxCh. 7.2 - Evaluate the integral. 26. 0/4sec6tan6dCh. 7.2 - Evaluate the integral. 27. tan3xsecxdxCh. 7.2 - Evaluate the integral. 28. tan5xsec3xdxCh. 7.2 - Evaluate the integral. 29. tan3xsec6xdxCh. 7.2 - Evaluate the integral. 30. 0/4tan3tdtCh. 7.2 - Evaluate the integral. 31. tan5xdxCh. 7.2 - Evaluate the integral. 32. tan2xsecxdxCh. 7.2 - Evaluate the integral. 33. 1tan2xsec2xdxCh. 7.2 - Evaluate the integral. 34. tanxsec2xcosxdxCh. 7.2 - Evaluate the integral. 35. 0/4sin3xcosxdxCh. 7.2 - Evaluate the integral. 36. sin+tancos3dCh. 7.2 - Evaluate the integral. 35. /6/2cot2xdxCh. 7.2 - Evaluate the integral. 36. /4/2cot3xdxCh. 7.2 - Evaluate the integral. 37. /4/2cot5csc3dCh. 7.2 - Evaluate the integral. 38. /4/2csc4cot4dCh. 7.2 - Evaluate the integral. 39. cscxdxCh. 7.2 - Evaluate the integral. 40. /6/3csc3xdxCh. 7.2 - Evaluate the integral. 41. sin8xcos5xdxCh. 7.2 - Evaluate the integral. 42. sin2sin6dCh. 7.2 - Evaluate the integral. 43. 0/2cot5tcos10tdtCh. 7.2 - Evaluate the integral. 46. tcos5t2dtCh. 7.2 - Evaluate the integral. 47. sin2(1/t)t2dtCh. 7.2 - Evaluate the integral. 48. sec2ycos3(tany)dyCh. 7.2 - Evaluate the integral. 45. 0/61+cos2xdxCh. 7.2 - Evaluate the integral. 46. 0/41cos4dCh. 7.2 - Evaluate the integral. 51. tsin2tdtCh. 7.2 - Evaluate the integral. 52. xsecxtanxdxCh. 7.2 - Evaluate the integral. 53. xtan2xdxCh. 7.2 - Evaluate the integral. 54. xsin3xdxCh. 7.2 - Evaluate the integral. 48. dxcosx1Ch. 7.2 - Evaluate the integral. 56. 1sec+1dCh. 7.2 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.2 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.2 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.2 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.2 - If 0/4tan6xsecxdx=I, , express the value of...Ch. 7.2 - Prob. 62ECh. 7.2 - Find the average value of the function f(x) =...Ch. 7.2 - Evaluate sin x cos x dx by four methods: (a) the...Ch. 7.2 - Find the area of the region bounded by the given...Ch. 7.2 - Find the area of the region bounded by the given...Ch. 7.2 - Use a graph of the integrand to guess the value of...Ch. 7.2 - Use a graph of the integrand to guess the value of...Ch. 7.2 - Find the volume obtained by rotating the region...Ch. 7.2 - Find the volume obtained by rotating the region...Ch. 7.2 - Find the volume obtained by rotating the region...Ch. 7.2 - Find the volume obtained by rotating the region...Ch. 7.2 - A particle moves on a straight line with velocity...Ch. 7.2 - Household electricity is supplied in the form of...Ch. 7.2 - Prove the formula, where m and n are positive...Ch. 7.2 - Prove the formula, where m and n are positive...Ch. 7.2 - Prove the formula, where m and n are positive...Ch. 7.2 - A finite Fourier series is given by the sum...Ch. 7.3 - a) Determine an appropriate trigonometric...Ch. 7.3 - (a) Determine an appropriate trigonometric...Ch. 7.3 - (a) Determine an appropriate trigonometric...Ch. 7.3 - (a) Determine an appropriate trigonometric...Ch. 7.3 - Evaluate the integral using the indicated...Ch. 7.3 - Evaluate the integral using the indicated...Ch. 7.3 - Evaluate the integral using the indicated...Ch. 7.3 - Evaluate the integral using the indicated...Ch. 7.3 - Evaluate the integral. 9. x316+x2dxCh. 7.3 - Evaluate the integral. 4. x29x2dxCh. 7.3 - Evaluate the integral. 5. x21x4dxCh. 7.3 - Evaluate the integral. 6. 03x36x2dxCh. 7.3 - Evaluate the integral. 7. 0adx(a2+x2)3/2, a 0Ch. 7.3 - Evaluate the integral. 8. dtt2t216Ch. 7.3 - Evaluate the integral. 9. 23dx(x21)3/2Ch. 7.3 - Evaluate the integral. 10. 02/349x2dxCh. 7.3 - Evaluate the integral. 11. 01/2x14x2dxCh. 7.3 - Evaluate the integral. 12. 02dt4+t2Ch. 7.3 - Evaluate the integral. 13. x29x3dxCh. 7.3 - Evaluate the integral. 14. 01dx(x2+1)2Ch. 7.3 - Evaluate the integral. 15. 0ax2a2x2dxCh. 7.3 - Evaluate the integral. 22. 1/43/414x2dxCh. 7.3 - Evaluate the integral. 17. xx27dxCh. 7.3 - Evaluate the integral. 24. x1+x2dxCh. 7.3 - Evaluate the integral. 19. 1+x2xdxCh. 7.3 - Evaluate the integral. 26. 00.3x925x23/2dxCh. 7.3 - Evaluate the integral. 21.00.6x2925x2dxCh. 7.3 - Evaluate the integral. 22. 01x2+1dxCh. 7.3 - Evaluate the integral. 23. dxx2+2x+5Ch. 7.3 - Evaluate the integral. 24. 01xx2dxCh. 7.3 - Evaluate the integral. 25. x23+2xx2dxCh. 7.3 - Evaluate the integral. 26. x2(3+4x4x2)3/2dxCh. 7.3 - Evaluate the integral. 27. x2+2xdxCh. 7.3 - Evaluate the integral. 28. x2+1(x22x+2)2dxCh. 7.3 - Evaluate the integral. 29. x1x4dxCh. 7.3 - Evaluate the integral. 30. 0/2cost1+sin2tdtCh. 7.3 - (a) Use trigonometric substitution to show that...Ch. 7.3 - Evaluate x2(x2+a2)3/2dx (a) by trigonometric...Ch. 7.3 - Find the average value of f(x)=x21/x, 1 x 1.Ch. 7.3 - Find the area of the region bounded by the...Ch. 7.3 - Prove the formula A = 12r2 for the area of a...Ch. 7.3 - Evaluate the integral dxx4x22 Graph the integrand...Ch. 7.3 - Find the volume of the solid obtained by rotating...Ch. 7.3 - Find the volume of the solid obtained by rotating...Ch. 7.3 - (a) Use trigonometric substitution to verify that...Ch. 7.3 - The parabola y = 12x2 divides the disk x2 + y2 8...Ch. 7.3 - A torus is generated by rotating the circle x2 +...Ch. 7.3 - A charged rod of length L produces an electric...Ch. 7.3 - Find the area of the crescent-shaped region...Ch. 7.3 - A water storage tank has the shape of a cylinder...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Write out the form of the partial fraction...Ch. 7.4 - Prob. 6ECh. 7.4 - Evaluate the integral. 7. 5(x1)(x+4)dxCh. 7.4 - Prob. 8ECh. 7.4 - Evaluate the integral. 9.5x+1(2x+1)(x1)dxCh. 7.4 - Evaluate the integral. 10.y(y+4)(2y1)dyCh. 7.4 - Evaluate the integral. 11.0122x2+3x+1dxCh. 7.4 - Evaluate the integral. 12.01x4x25x+6dxCh. 7.4 - Evaluate the integral. 13. 1x(xa)dxCh. 7.4 - Evaluate the integral. 14.1(x+a)(x+b)dxCh. 7.4 - Evaluate the integral. 15. x2x1dxCh. 7.4 - Prob. 16ECh. 7.4 - Evaluate the integral. 17.124y27y12y(y+2)(y3)dyCh. 7.4 - Evaluate the integral. 18.123x2+6x+2x2+3x+2dxCh. 7.4 - Evaluate the integral. 19.01x2+x+1(x+1)2(x+2)dxCh. 7.4 - Evaluate the integral. 20.23x(35x)(3x1)(x1)2dxCh. 7.4 - Evaluate the integral. 21.dt(t21)2Ch. 7.4 - Prob. 22ECh. 7.4 - Evaluate the integral. 23.10(x1)(x2+9)dxCh. 7.4 - Evaluate the integral. 24. 3x2x+8x3+4xdxCh. 7.4 - Evaluate the integral. 25. 10x34x+1x23x+2dxCh. 7.4 - Evaluate the integral. 26. 12x3+4x2+x1x3+x2dxCh. 7.4 - Evaluate the integral. 25.4xx3+x2+x+1dxCh. 7.4 - Evaluate the integral. 26.x2+x+1(x2+1)2dxCh. 7.4 - Evaluate the integral. 27.x3+4x+3x4+5x2+4dxCh. 7.4 - Evaluate the integral. 28.x3+6x2x4+6x2dxCh. 7.4 - Evaluate the integral. 29.x+4x2+2x+5dxCh. 7.4 - Evaluate the integral. 32. 01xx2+4x+13dxCh. 7.4 - Evaluate the integral. 33. 1x31dxCh. 7.4 - Evaluate the integral. 30.x32x2+2x5x4+4x2+3dxCh. 7.4 - Evaluate the integral. 33.01x3+2xx4+4x2+3dxCh. 7.4 - Evaluate the integral. 34.x5+x1x3+1dxCh. 7.4 - Evaluate the integral. 35.5x4+7x2+x+2x(x2+1)2dxCh. 7.4 - Evaluate the integral. 36.x4+3x2+1x5+5x3+5xdxCh. 7.4 - Evaluate the integral. 37.x23x+7(x24x+6)2dxCh. 7.4 - Evaluate the integral. 38.x3+2x2+3x2(x2+2x+2)2dxCh. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Prob. 48ECh. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Prob. 54ECh. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Prob. 56ECh. 7.4 - Use integration by parts, together with the...Ch. 7.4 - Prob. 58ECh. 7.4 - Use a graph of f(x) = 1/(x2 2x 3) to decide...Ch. 7.4 - Evaluate 1x2+kdx by considering several cases for...Ch. 7.4 - Evaluate the integral by completing the square and...Ch. 7.4 - Prob. 62ECh. 7.4 - Find the area of the region under the given curve...Ch. 7.4 - Find the area of the region under the given curve...Ch. 7.4 - Find the volume of the resulting solid if the...Ch. 7.4 - One method of slowing the growth of an insect...Ch. 7.4 - Prob. 72ECh. 7.4 - Prob. 73ECh. 7.4 - Suppose that F, G, and Q are polynomials and...Ch. 7.4 - If a 0 and n is a positive integer, find the...Ch. 7.4 - If f is a quadratic function such that f(0) = 1...Ch. 7.5 - Three integrals are given that, although they look...Ch. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Three integrals are given that, although they look...Ch. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Evaluate the integral. 1. cosx1sinxdxCh. 7.5 - Evaluate the integral. 2. 01(3x+1)2dxCh. 7.5 - Evaluate the integral. 3. 14ylnydyCh. 7.5 - Prob. 12ECh. 7.5 - Prob. 13ECh. 7.5 - Evaluate the integral. 6. 01x(2x+1)3dxCh. 7.5 - Prob. 15ECh. 7.5 - Evaluate the integral. 8. tsintcostdtCh. 7.5 - Evaluate the integral. 9. 24x+2x2+3x4dxCh. 7.5 - Evaluate the integral. 10. cos(1/x)x3dxCh. 7.5 - Evaluate the integral. 11. 1x3x21dxCh. 7.5 - Evaluate the integral. 12. 2x3x3+3xdxCh. 7.5 - Prob. 21ECh. 7.5 - Evaluate the integral. 14. ln(1+x2)dxCh. 7.5 - Evaluate the integral. 15. xsecxtanxdxCh. 7.5 - Evaluate the integral. 16. 02/2x21x2dxCh. 7.5 - Evaluate the integral. 17. 0tcos2tdtCh. 7.5 - Prob. 26ECh. 7.5 - Evaluate the integral. 19. ex+exdxCh. 7.5 - Prob. 28ECh. 7.5 - Evaluate the integral. 21. arctanxdxCh. 7.5 - Evaluate the integral. 22. lnxx1+(lnx)2dxCh. 7.5 - Evaluate the integral. 23. 01(1+x)8dxCh. 7.5 - Evaluate the integral. 24. (1+tanx)2secxdxCh. 7.5 - Evaluate the integral. 25. 011+12t1+3tdtCh. 7.5 - Evaluate the integral. 26. 013x2+1x3+x2+x+1dxCh. 7.5 - Evaluate the integral. 27. dx1+exCh. 7.5 - Evaluate the integral. 28. sinatdtCh. 7.5 - Evaluate the integral. 29. ln(x+x21)dxCh. 7.5 - Evaluate the integral. 30. 12|ex1|dxCh. 7.5 - Prob. 39ECh. 7.5 - Prob. 40ECh. 7.5 - Evaluate the integral. 33. 32xx2dxCh. 7.5 - Evaluate the integral. 34. /4/21+4cotx4cotxdxCh. 7.5 - Prob. 43ECh. 7.5 - Prob. 44ECh. 7.5 - Prob. 45ECh. 7.5 - Prob. 46ECh. 7.5 - Prob. 47ECh. 7.5 - Prob. 48ECh. 7.5 - Prob. 49ECh. 7.5 - Evaluate the integral. 50. 1xx1dxCh. 7.5 - Prob. 51ECh. 7.5 - Evaluate the integral. 44. 1+exdxCh. 7.5 - Evaluate the integral. 53. x1+xdxCh. 7.5 - Evaluate the integral. 46. (x1)exx2dxCh. 7.5 - Evaluate the integral. 47. x3(x1)4dxCh. 7.5 - Prob. 56ECh. 7.5 - Evaluate the integral. 49. 1x4x+1dxCh. 7.5 - Prob. 58ECh. 7.5 - Prob. 59ECh. 7.5 - Evaluate the integral. 52. dxxx4+1Ch. 7.5 - Prob. 61ECh. 7.5 - Prob. 62ECh. 7.5 - Evaluate the integral. 55. dxx+xxCh. 7.5 - Evaluate the integral. 56. dxx+xxCh. 7.5 - Prob. 65ECh. 7.5 - Prob. 66ECh. 7.5 - Prob. 67ECh. 7.5 - Prob. 68ECh. 7.5 - Evaluate the integral. 61. d1+cosCh. 7.5 - Prob. 70ECh. 7.5 - Prob. 71ECh. 7.5 - Prob. 72ECh. 7.5 - Prob. 73ECh. 7.5 - Prob. 74ECh. 7.5 - Prob. 75ECh. 7.5 - Prob. 76ECh. 7.5 - Evaluate the integral. 69. 131+x2x2dxCh. 7.5 - Evaluate the integral. 70. 11+2exexdxCh. 7.5 - Evaluate the integral. 71. e2x1+exdxCh. 7.5 - Prob. 80ECh. 7.5 - Evaluate the integral. 73. x+arcsinx1x2dxCh. 7.5 - Prob. 82ECh. 7.5 - Prob. 83ECh. 7.5 - Prob. 84ECh. 7.5 - Prob. 85ECh. 7.5 - Evaluate the integral. 78. 1+sinx1sinxdxCh. 7.5 - Prob. 87ECh. 7.5 - Prob. 88ECh. 7.5 - Prob. 89ECh. 7.5 - Prob. 90ECh. 7.5 - Prob. 91ECh. 7.5 - Prob. 92ECh. 7.5 - Prob. 93ECh. 7.5 - Prob. 94ECh. 7.5 - Prob. 95ECh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Use the formula in the indicated entry of the...Ch. 7.6 - Prob. 5ECh. 7.6 - Prob. 6ECh. 7.6 - Prob. 7ECh. 7.6 - Prob. 8ECh. 7.6 - Prob. 9ECh. 7.6 - Prob. 10ECh. 7.6 - Prob. 11ECh. 7.6 - Prob. 12ECh. 7.6 - Prob. 13ECh. 7.6 - Prob. 14ECh. 7.6 - Prob. 15ECh. 7.6 - Prob. 16ECh. 7.6 - Prob. 17ECh. 7.6 - Prob. 18ECh. 7.6 - Prob. 20ECh. 7.6 - Prob. 21ECh. 7.6 - Prob. 22ECh. 7.6 - Prob. 23ECh. 7.6 - Prob. 24ECh. 7.6 - Prob. 25ECh. 7.6 - Prob. 26ECh. 7.6 - Prob. 27ECh. 7.6 - Prob. 28ECh. 7.6 - Prob. 29ECh. 7.6 - Prob. 30ECh. 7.6 - Prob. 31ECh. 7.6 - Prob. 32ECh. 7.6 - Prob. 33ECh. 7.6 - Prob. 34ECh. 7.6 - The region under the curve y = sin2 x from 0 to ...Ch. 7.6 - Find the volume of the solid obtained when the...Ch. 7.6 - Verify Formula 53 in the Table of Integrals (a) by...Ch. 7.6 - Verify Formula 31 (a) by differentiation and (b)...Ch. 7.7 - Prob. 7ECh. 7.7 - Prob. 8ECh. 7.7 - Prob. 9ECh. 7.7 - Prob. 11ECh. 7.7 - Prob. 12ECh. 7.7 - Prob. 13ECh. 7.7 - Prob. 15ECh. 7.7 - Prob. 16ECh. 7.7 - Prob. 17ECh. 7.7 - Prob. 18ECh. 7.7 - Prob. 26ECh. 7.7 - Prob. 29ECh. 7.7 - Prob. 30ECh. 7.7 - Prob. 31ECh. 7.7 - Prob. 32ECh. 7.7 - Prob. 33ECh. 7.7 - Prob. 34ECh. 7.7 - Prob. 35ECh. 7.7 - Prob. 36ECh. 7.7 - Prob. 37ECh. 7.7 - Prob. 38ECh. 7.7 - Prob. 39ECh. 7.7 - Prob. 40ECh. 7.7 - Prob. 41ECh. 7.7 - Prob. 42ECh. 7.7 - Prob. 43ECh. 7.7 - Prob. 44ECh. 7.8 - Find the area under the curve y = 1/x3 from x = 1...Ch. 7.8 - Prob. 4ECh. 7.8 - Determine whether the integral is Evaluate...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Prob. 8ECh. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Prob. 10ECh. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Determine whether each integral is convergent or...Ch. 7.8 - Sketch the region and find its area (if the area...Ch. 7.8 - Prob. 50ECh. 7.8 - Sketch the region and find its area (if the area...Ch. 7.8 - Sketch the region and find its area (if the area...Ch. 7.8 - Sketch the region and find its area (if the area...Ch. 7.8 - Sketch the region and find its area (if the area...Ch. 7.8 - Prob. 55ECh. 7.8 - Prob. 56ECh. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Prob. 59ECh. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Prob. 62ECh. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Improper Integrals that Are Both Type 1 and Type 2...Ch. 7.8 - Prob. 66ECh. 7.8 - Improper Integrals that Are Both Type 1 and Type 2...Ch. 7.8 - Improper Integrals that Are Both Type 1 and Type 2...Ch. 7.8 - Find the values of p for which the integral...Ch. 7.8 - Find the values of p for which the integral...Ch. 7.8 - Find the values of p for which the integral...Ch. 7.8 - (a) Evaluate the integral 0xnexdx for n = 0, 1, 2,...Ch. 7.8 - Prob. 73ECh. 7.8 - The average speed of molecules in an ideal gas is...Ch. 7.8 - We know from Example 1 that the region R = {(x, y)...Ch. 7.8 - Prob. 76ECh. 7.8 - Find the escape velocity v0 that is needed to...Ch. 7.8 - Astronomers use a technique called stellar...Ch. 7.8 - A manufacturer of lightbulbs wants to produce...Ch. 7.8 - As we saw in Section 3.8, a radioactive substance...Ch. 7.8 - In a study of the spread of illicit drug use from...Ch. 7.8 - Dialysis treatment removes urea and other waste...Ch. 7.8 - Determine how large the number a has to be so that...Ch. 7.8 - Estimate the numerical value of 0ex2dx by writing...Ch. 7.8 - Prob. 85ECh. 7.8 - Prob. 86ECh. 7.8 - Prob. 87ECh. 7.8 - Prob. 88ECh. 7.8 - Show that 0x2ex2dx=120ex2dx.Ch. 7.8 - Prob. 90ECh. 7.8 - Find the value of the constant C for which the...Ch. 7.8 - Find the value of the constant C for which the...Ch. 7.8 - Suppose f is continuous on [0, ) and limxf(x) = 1....Ch. 7.8 - Show that if a 1 and b a + 1, then the...Ch. 7 - Stale the rule for integration by parts. In...Ch. 7 - How do you evaluate sinmxcosnxdx if m is odd? What...Ch. 7 - If the expression a2x2 occurs in an integral, what...Ch. 7 - Prob. 4CCCh. 7 - Prob. 5CCCh. 7 - Prob. 6CCCh. 7 - Define the improper integral abf(x)dx for each of...Ch. 7 - State the Comparison Theorem for improper...Ch. 7 - Prob. 1TFQCh. 7 - Determine whether the statement is true or false....Ch. 7 - Prob. 3TFQCh. 7 - Prob. 4TFQCh. 7 - Determine whether the statement is true or false....Ch. 7 - Prob. 6TFQCh. 7 - Prob. 7TFQCh. 7 - Prob. 8TFQCh. 7 - Prob. 9TFQCh. 7 - Prob. 10TFQCh. 7 - Prob. 11TFQCh. 7 - Determine whether the statement is true or false....Ch. 7 - Determine whether the statement is true or false....Ch. 7 - Determine whether the statement is true or false....Ch. 7 - Prob. 15TFQCh. 7 - Prob. 16TFQCh. 7 - Determine whether the statement is true or false....Ch. 7 - Prob. 18TFQCh. 7 - Evaluate the integral. 1. 12(x+1)2xdxCh. 7 - Evaluate the integral. 2. 12x(x+1)2dxCh. 7 - Prob. 3ECh. 7 - Prob. 4ECh. 7 - Evaluate the integral. 5. dt2t2+3t+1Ch. 7 - Evaluate the integral. 6. 12x5lnxdxCh. 7 - Prob. 7ECh. 7 - Prob. 8ECh. 7 - Prob. 9ECh. 7 - Prob. 10ECh. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - Evaluate the integral. 11. 12x21xdxCh. 7 - Prob. 14ECh. 7 - Evaluate the integral. 13. ex3dxCh. 7 - Prob. 16ECh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - Evaluate the integral. 15. x1x2+2xdxCh. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Evaluate the integral. 19. x+19x2+6x+5dxCh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Prob. 28ECh. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Prob. 33ECh. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Prob. 37ECh. 7 - Prob. 38ECh. 7 - Prob. 39ECh. 7 - Evaluate the integral. 32. 0/4xsinxcos3xdxCh. 7 - Evaluate the integral. 33. x2(4x2)3/2dxCh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - Prob. 44ECh. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Prob. 51ECh. 7 - Prob. 52ECh. 7 - Prob. 53ECh. 7 - Evaluate the integral or show that it is...Ch. 7 - Prob. 55ECh. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58ECh. 7 - Evaluate the integral or show that it is...Ch. 7 - Evaluate the integral or show that it is...Ch. 7 - Evaluate the indefinite integral. Illustrate and...Ch. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - Prob. 64ECh. 7 - Prob. 65ECh. 7 - Prob. 66ECh. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - Prob. 70ECh. 7 - Prob. 71ECh. 7 - For what values of a is 0eaxcosxdx convergent?...Ch. 7 - Use (a) the Trapezoidal Rule, (b) the Midpoint...Ch. 7 - Prob. 74ECh. 7 - Prob. 75ECh. 7 - Prob. 76ECh. 7 - Prob. 77ECh. 7 - Prob. 78ECh. 7 - Prob. 79ECh. 7 - Prob. 80ECh. 7 - Prob. 81ECh. 7 - Prob. 82ECh. 7 - Prob. 83ECh. 7 - Prob. 84ECh. 7 - The region under the curve y = cos2x, 0 x /2, is...Ch. 7 - Prob. 86ECh. 7 - Prob. 87ECh. 7 - Prob. 88ECh. 7 - Prob. 89ECh. 7 - Prob. 90ECh. 7 - Prob. 1PCh. 7 - Evaluate 1x7xdx The straightforward approach would...Ch. 7 - Prob. 3PCh. 7 - Prob. 5PCh. 7 - The centers of two disks with radius 1 are one...Ch. 7 - Prob. 7PCh. 7 - A man initially standing at the point O walks...Ch. 7 - A function f is defined by f(x)=0costcos(xt)dt0x2...Ch. 7 - If n is a positive integer, prove that...Ch. 7 - Show that 01(1x2)ndx=22n(n!)2(2n+1)! Hint: Start...Ch. 7 - Prob. 12PCh. 7 - If 0 a b, find limt0{01[bx+a(1x)]tdx}1/tCh. 7 - Prob. 14PCh. 7 - Prob. 15PCh. 7 - Prob. 16PCh. 7 - The circle with radius 1 shown in the figure...Ch. 7 - Prob. 18P
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- Construct a table and find the indicated limit. √√x+2 If h(x) = then find lim h(x). X-8 X-8 Complete the table below. X 7.9 h(x) 7.99 7.999 8.001 8.01 8.1 (Type integers or decimals rounded to four decimal places as needed.)arrow_forwardUse the graph to find the following limits. (a) lim f(x) (b) lim f(x) X-1 x→1 (a) Find lim f(x) or state that it does not exist. Select the correct choice X-1 below and, if necessary, fill in the answer box within your choice. OA. lim f(x) = X-1 (Round to the nearest integer as needed.) OB. The limit does not exist. Qarrow_forwardOfficials in a certain region tend to raise the sales tax in years in which the state faces a budget deficit and then cut the tax when the state has a surplus. The graph shows the region's sales tax in recent years. Let T(x) represent the sales tax per dollar spent in year x. Find the desired limits and values, if they exist. Note that '01 represents 2001. Complete parts (a) through (e). Tax (in cents) T(X)4 8.5 8- OA. lim T(x)= cent(s) X-2007 (Type an integer or a decimal.) OB. The limit does not exist and is neither ∞ nor - ∞. Garrow_forward
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- Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. 8+x f(x) = x(x-1) (Use a comma to separate answers as needed.) OA. The function f is discontinuous at the single value x = OB. The function f is discontinuous at the single value x = OC. The function f is discontinuous at the two values x = OD. The function f is discontinuous at the two values x = not oo or -0. OE. The function f is discontinuous at the two values x = The limit is The limit does not exist and is not oo or - co. The limits for both values do not exist and are not co or - co. The limit for the smaller value is The limit for the larger value does not exist and is The limit for the smaller value does not exist and is not co or - co. The limit for the largerarrow_forwardi need help please . and please dont use chat gpt i am trying to learn and see the mistake i did when solving minearrow_forwardi need help please . and please dont use chat gpt i am trying to learn and see the mistake i did when solving minearrow_forward
- The radius of a sphere decreases at a rate of 3 m/s. Find the rate at which the surface area decreases when the radius is 8 m. Answer exactly or round to 2 decimal places. The surface area decreases at a rate of m²/sarrow_forwardi need help pleasearrow_forward(#1) Consider the solid bounded below by z = x² and above by z = 4-y². If we were to project this solid down onto the xy-plane, you should be able to use algebra to determine the 2D region R in the xy-plane for the purposes of integration. Which ONE of these limite of integration would correctly describe R? (a) y: x24x: -22 - (b) y: 22 x: 04-y² (c) y: -√√4-x2. →√√4x²x: −2 → 2 (d) z: 24-y² y: -2 → 2 (e) None of the abovearrow_forward
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