Calculus, Early Transcendentals
Calculus, Early Transcendentals
9th Edition
ISBN: 9781337613927
Author: Stewart
Publisher: CENGAGE L
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Concept explainers

Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
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Chapter 7.5, Problem 1E

Three integrals are given that, although they look similar, may require different techniques of integration. Evaluate the integrals.

1. (a) ∫ x 1 + x 2 d x

(b) ∫ 1 1 + x 2 d x

(c) ∫ 1 1 − x 2 d x

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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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