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Math Calculus Calculus, Early Transcendentals

Use Exercise 58 to find ∫ x 4 e x d x . 58. ∫ x n e x d x = x n e x − n ∫ x n − 1 e x d x

Use Exercise 58 to find ∫ x 4 e x d x . 58. ∫ x n e x d x = x n e x − n ∫ x n − 1 e x d x

Solution Summary: The author explains how to evaluate the integral using a reduction formula.

Calculus, Early Transcendentals

Calculus, Early Transcendentals

9th Edition

ISBN: 9781337613927

Author: Stewart

Publisher: CENGAGE L

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Textbook Question

Chapter 7.1, Problem 62E

Use Exercise 58 to find ∫ x 4 e x d x .

58. ∫ x n e x d x = x n e x − n ∫ x n − 1 e x d x

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Chapter 7.1, Problem 61E

Chapter 7.1, Problem 63E

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Evaluate x(x2 + 1)3 dx.

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. yeydy Ch. 7.1 - Evaluate the integral. 7. xsin10xdx Ch. 7.1 - Evaluate the integral. 8. (x)cosxdx Ch. 7.1 - Evaluate the integral. 9. wlnwdw Ch. 7.1 - Evaluate the integral. 10. lnxx2dx Ch. 7.1 - Evaluate the integral. 7. (x2+2x)cosxdx

Ch. 7.1 - Evaluate the integral. 8. t2sintdt Ch. 7.1 - Evaluate the integral. 9. cos1xdx Ch. 7.1 - Evaluate the integral. 10. lnxdx Ch. 7.1 - Evaluate the integral. 11. t4lntdt Ch. 7.1 - Evaluate the integral. 12. tan12ydy Ch. 7.1 - Evaluate the integral. 13. tcsc2tdt Ch. 7.1 - Evaluate the integral. 14. xcoshaxdx Ch. 7.1 - Evaluate the integral. 15. (lnx)2dx Ch. 7.1 - Evaluate the integral. 16. z10zdz Ch. 7.1 - Evaluate the integral. 21. e3xcosxdx Ch. 7.1 - Evaluate the integral. 22. exsinxdx Ch. 7.1 - Evaluate the integral. 17. e2sin3d Ch. 7.1 - Evaluate the integral. 18. ecos2d Ch. 7.1 - Evaluate the integral. 19. z3ezdz Ch. 7.1 - Evaluate the integral. 22. (arcsinx)2dx Ch. 7.1 - Evaluate the integral. 27. 1+x2e3xdx Ch. 7.1 - Evaluate the integral. 28. 01/2sin3d Ch. 7.1 - Evaluate the integral. 29. 01x3xdx Ch. 7.1 - Evaluate the integral. 30. 01xex(1+x)2dx Ch. 7.1 - Evaluate the integral. 25. 02ysinhydy Ch. 7.1 - Evaluate the integral. 26. 12w2lnwdw Ch. 7.1 - Evaluate the integral. 27. 15lnRR2dR Ch. 7.1 - Evaluate the integral. 28. 02t2sin2tdt Ch. 7.1 - Evaluate the integral. 29. 0xsinxcosxdx Ch. 7.1 - Evaluate the integral. 30. 13arctan(1/x)dx Ch. 7.1 - Evaluate the integral. 31. 15MeMdM Ch. 7.1 - Evaluate the integral. 32. 12(lnx)2x3dx Ch. 7.1 - Evaluate the integral. 33. 0/3sinxln(cosx)dx Ch. 7.1 - Evaluate the integral. 34. 01r34+r2dr Ch. 7.1 - Evaluate the integral. 41. 0cosxsinhxdx Ch. 7.1 - Evaluate the integral. 36. 0tessin(ts)ds 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 - 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. 70E Ch. 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. 76E Ch. 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. 79E Ch. 7.1 - We arrived at Formula 6.3.2, V=ab2xf(x)dx, by...Ch. 7.2 - Evaluate the integral. 1. sin3xcos2xdx Ch. 7.2 - Evaluate the integral. 2. cos6ysin3ydy Ch. 7.2 - Evaluate the integral. 3. 0/2cos9xsin5xdx Ch. 7.2 - Evaluate the integral. 4. 0/4sin5xdx Ch. 7.2 - Evaluate the integral. 5. sin5(2t)cos2(2t)dt Ch. 7.2 - Evaluate the integral. 6. cos3(t/2)sin2(t/2)dt Ch. 7.2 - Evaluate the integral. 7. 0/2cos2d Ch. 7.2 - Evaluate the integral. 8. 0/4sin2(2)d Ch. 7.2 - Evaluate the integral. 9. 0cos4(2t)dt Ch. 7.2 - Evaluate the integral. 10. 0sin2tcos4tdt Ch. 7.2 - Evaluate the integral. 11. 0/2sin2xcos2xdx Ch. 7.2 - Evaluate the integral. 12. 0/2(2sin)2d Ch. 7.2 - Evaluate the integral. 13. cossin3d Ch. 7.2 - Evaluate the integral. 14. (1+sint3)cos3tdt Ch. 7.2 - Evaluate the integral. 15. sinxsec5xdx Ch. 7.2 - Evaluate the integral. 16. csc5cos3d Ch. 7.2 - Evaluate the integral. 15. cotxcos2xdx Ch. 7.2 - Evaluate the integral. 16. tan2xcos3xdx Ch. 7.2 - Evaluate the integral. 17. sin2xsin2xdx Ch. 7.2 - Evaluate the integral. 18. sinxcos(12x)dx Ch. 7.2 - Evaluate the integral. 21. tanxsec3xdx Ch. 7.2 - Evaluate the integral. 22. tan2sec4d Ch. 7.2 - Evaluate the integral. 23. tan2xdx Ch. 7.2 - Evaluate the integral. 24. (tan2x+tan4x)dx Ch. 7.2 - Evaluate the integral. 25. tan4xsec6xdx Ch. 7.2 - Evaluate the integral. 26. 0/4sec6tan6d Ch. 7.2 - Evaluate the integral. 27. tan3xsecxdx Ch. 7.2 - Evaluate the integral. 28. tan5xsec3xdx Ch. 7.2 - Evaluate the integral. 29. tan3xsec6xdx Ch. 7.2 - Evaluate the integral. 30. 0/4tan3tdt Ch. 7.2 - Evaluate the integral. 31. tan5xdx Ch. 7.2 - Evaluate the integral. 32. tan2xsecxdx Ch. 7.2 - Evaluate the integral. 33. 1tan2xsec2xdx Ch. 7.2 - Evaluate the integral. 34. tanxsec2xcosxdx Ch. 7.2 - Evaluate the integral. 35. 0/4sin3xcosxdx Ch. 7.2 - Evaluate the integral. 36. sin+tancos3d Ch. 7.2 - Evaluate the integral. 35. /6/2cot2xdx Ch. 7.2 - Evaluate the integral. 36. /4/2cot3xdx Ch. 7.2 - Evaluate the integral. 37. /4/2cot5csc3d Ch. 7.2 - Evaluate the integral. 38. /4/2csc4cot4d Ch. 7.2 - Evaluate the integral. 39. cscxdx Ch. 7.2 - Evaluate the integral. 40. /6/3csc3xdx Ch. 7.2 - Evaluate the integral. 41. sin8xcos5xdx Ch. 7.2 - Evaluate the integral. 42. sin2sin6d Ch. 7.2 - Evaluate the integral. 43. 0/2cot5tcos10tdt Ch. 7.2 - Evaluate the integral. 46. tcos5t2dt Ch. 7.2 - Evaluate the integral. 47. sin2(1/t)t2dt Ch. 7.2 - Evaluate the integral. 48. sec2ycos3(tany)dy Ch. 7.2 - Evaluate the integral. 45. 0/61+cos2xdx Ch. 7.2 - Evaluate the integral. 46. 0/41cos4d Ch. 7.2 - Evaluate the integral. 51. tsin2tdt Ch. 7.2 - Evaluate the integral. 52. xsecxtanxdx Ch. 7.2 - Evaluate the integral. 53. xtan2xdx Ch. 7.2 - Evaluate the integral. 54. xsin3xdx Ch. 7.2 - Evaluate the integral. 48. dxcosx1 Ch. 7.2 - Evaluate the integral. 56. 1sec+1d 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 - Evaluate the indefinite integral. Illustrate, and...Ch. 7.2 - If 0/4tan6xsecxdx=I, , express the value of...Ch. 7.2 - Prob. 62E Ch. 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+x2dx Ch. 7.3 - Evaluate the integral. 4. x29x2dx Ch. 7.3 - Evaluate the integral. 5. x21x4dx Ch. 7.3 - Evaluate the integral. 6. 03x36x2dx Ch. 7.3 - Evaluate the integral. 7. 0adx(a2+x2)3/2, a 0 Ch. 7.3 - Evaluate the integral. 8. dtt2t216 Ch. 7.3 - Evaluate the integral. 9. 23dx(x21)3/2 Ch. 7.3 - Evaluate the integral. 10. 02/349x2dx Ch. 7.3 - Evaluate the integral. 11. 01/2x14x2dx Ch. 7.3 - Evaluate the integral. 12. 02dt4+t2 Ch. 7.3 - Evaluate the integral. 13. x29x3dx Ch. 7.3 - Evaluate the integral. 14. 01dx(x2+1)2 Ch. 7.3 - Evaluate the integral. 15. 0ax2a2x2dx Ch. 7.3 - Evaluate the integral. 22. 1/43/414x2dx Ch. 7.3 - Evaluate the integral. 17. xx27dx Ch. 7.3 - Evaluate the integral. 24. x1+x2dx Ch. 7.3 - Evaluate the integral. 19. 1+x2xdx Ch. 7.3 - Evaluate the integral. 26. 00.3x925x23/2dx Ch. 7.3 - Evaluate the integral. 21.00.6x2925x2dx Ch. 7.3 - Evaluate the integral. 22. 01x2+1dx Ch. 7.3 - Evaluate the integral. 23. dxx2+2x+5 Ch. 7.3 - Evaluate the integral. 24. 01xx2dx Ch. 7.3 - Evaluate the integral. 25. x23+2xx2dx Ch. 7.3 - Evaluate the integral. 26. x2(3+4x4x2)3/2dx Ch. 7.3 - Evaluate the integral. 27. x2+2xdx Ch. 7.3 - Evaluate the integral. 28. x2+1(x22x+2)2dx Ch. 7.3 - Evaluate the integral. 29. x1x4dx Ch. 7.3 - Evaluate the integral. 30. 0/2cost1+sin2tdt Ch. 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. 6E Ch. 7.4 - Evaluate the integral. 7. 5(x1)(x+4)dx Ch. 7.4 - Prob. 8E Ch. 7.4 - Evaluate the integral. 9.5x+1(2x+1)(x1)dx Ch. 7.4 - Evaluate the integral. 10.y(y+4)(2y1)dy Ch. 7.4 - Evaluate the integral. 11.0122x2+3x+1dx Ch. 7.4 - Evaluate the integral. 12.01x4x25x+6dx Ch. 7.4 - Evaluate the integral. 13. 1x(xa)dx Ch. 7.4 - Evaluate the integral. 14.1(x+a)(x+b)dx Ch. 7.4 - Evaluate the integral. 15. x2x1dx Ch. 7.4 - Prob. 16E Ch. 7.4 - Evaluate the integral. 17.124y27y12y(y+2)(y3)dy Ch. 7.4 - Evaluate the integral. 18.123x2+6x+2x2+3x+2dx Ch. 7.4 - Evaluate the integral. 19.01x2+x+1(x+1)2(x+2)dx Ch. 7.4 - Evaluate the integral. 20.23x(35x)(3x1)(x1)2dx Ch. 7.4 - Evaluate the integral. 21.dt(t21)2 Ch. 7.4 - Prob. 22E Ch. 7.4 - Evaluate the integral. 23.10(x1)(x2+9)dx Ch. 7.4 - Evaluate the integral. 24. 3x2x+8x3+4xdx Ch. 7.4 - Evaluate the integral. 25. 10x34x+1x23x+2dx Ch. 7.4 - Evaluate the integral. 26. 12x3+4x2+x1x3+x2dx Ch. 7.4 - Evaluate the integral. 25.4xx3+x2+x+1dx Ch. 7.4 - Evaluate the integral. 26.x2+x+1(x2+1)2dx Ch. 7.4 - Evaluate the integral. 27.x3+4x+3x4+5x2+4dx Ch. 7.4 - Evaluate the integral. 28.x3+6x2x4+6x2dx Ch. 7.4 - Evaluate the integral. 29.x+4x2+2x+5dx Ch. 7.4 - Evaluate the integral. 32. 01xx2+4x+13dx Ch. 7.4 - Evaluate the integral. 33. 1x31dx Ch. 7.4 - Evaluate the integral. 30.x32x2+2x5x4+4x2+3dx Ch. 7.4 - Evaluate the integral. 33.01x3+2xx4+4x2+3dx Ch. 7.4 - Evaluate the integral. 34.x5+x1x3+1dx Ch. 7.4 - Evaluate the integral. 35.5x4+7x2+x+2x(x2+1)2dx Ch. 7.4 - Evaluate the integral. 36.x4+3x2+1x5+5x3+5xdx Ch. 7.4 - Evaluate the integral. 37.x23x+7(x24x+6)2dx Ch. 7.4 - Evaluate the integral. 38.x3+2x2+3x2(x2+2x+2)2dx 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 - Make a substitution to express the integrand as a...Ch. 7.4 - Prob. 48E 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. 54E Ch. 7.4 - Make a substitution to express the integrand as a...Ch. 7.4 - Prob. 56E Ch. 7.4 - Use integration by parts, together with the...Ch. 7.4 - Prob. 58E Ch. 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. 62E Ch. 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. 72E Ch. 7.4 - Prob. 73E Ch. 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. 2E Ch. 7.5 - Prob. 3E Ch. 7.5 - Three integrals are given that, although they look...Ch. 7.5 - Prob. 6E Ch. 7.5 - Prob. 7E Ch. 7.5 - Prob. 8E Ch. 7.5 - Evaluate the integral. 1. cosx1sinxdx Ch. 7.5 - Evaluate the integral. 2. 01(3x+1)2dx Ch. 7.5 - Evaluate the integral. 3. 14ylnydy Ch. 7.5 - Prob. 12E Ch. 7.5 - Prob. 13E Ch. 7.5 - Evaluate the integral. 6. 01x(2x+1)3dx Ch. 7.5 - Prob. 15E Ch. 7.5 - Evaluate the integral. 8. tsintcostdt Ch. 7.5 - Evaluate the integral. 9. 24x+2x2+3x4dx Ch. 7.5 - Evaluate the integral. 10. cos(1/x)x3dx Ch. 7.5 - Evaluate the integral. 11. 1x3x21dx Ch. 7.5 - Evaluate the integral. 12. 2x3x3+3xdx Ch. 7.5 - Prob. 21E Ch. 7.5 - Evaluate the integral. 14. ln(1+x2)dx Ch. 7.5 - Evaluate the integral. 15. xsecxtanxdx Ch. 7.5 - Evaluate the integral. 16. 02/2x21x2dx Ch. 7.5 - Evaluate the integral. 17. 0tcos2tdt Ch. 7.5 - Prob. 26E Ch. 7.5 - Evaluate the integral. 19. ex+exdx Ch. 7.5 - Prob. 28E Ch. 7.5 - Evaluate the integral. 21. arctanxdx Ch. 7.5 - Evaluate the integral. 22. lnxx1+(lnx)2dx Ch. 7.5 - Evaluate the integral. 23. 01(1+x)8dx Ch. 7.5 - Evaluate the integral. 24. (1+tanx)2secxdx Ch. 7.5 - Evaluate the integral. 25. 011+12t1+3tdt Ch. 7.5 - Evaluate the integral. 26. 013x2+1x3+x2+x+1dx Ch. 7.5 - Evaluate the integral. 27. dx1+ex Ch. 7.5 - Evaluate the integral. 28. sinatdt Ch. 7.5 - Evaluate the integral. 29. ln(x+x21)dx Ch. 7.5 - Evaluate the integral. 30. 12|ex1|dx Ch. 7.5 - Prob. 39E Ch. 7.5 - Prob. 40E Ch. 7.5 - Evaluate the integral. 33. 32xx2dx Ch. 7.5 - Evaluate the integral. 34. /4/21+4cotx4cotxdx Ch. 7.5 - Prob. 43E Ch. 7.5 - Prob. 44E Ch. 7.5 - Prob. 45E Ch. 7.5 - Prob. 46E Ch. 7.5 - Prob. 47E Ch. 7.5 - Prob. 48E Ch. 7.5 - Prob. 49E Ch. 7.5 - Evaluate the integral. 50. 1xx1dx Ch. 7.5 - Prob. 51E Ch. 7.5 - Evaluate the integral. 44. 1+exdx Ch. 7.5 - Evaluate the integral. 53. x1+xdx Ch. 7.5 - Evaluate the integral. 46. (x1)exx2dx Ch. 7.5 - Evaluate the integral. 47. x3(x1)4dx Ch. 7.5 - Prob. 56E Ch. 7.5 - Evaluate the integral. 49. 1x4x+1dx Ch. 7.5 - Prob. 58E Ch. 7.5 - Prob. 59E Ch. 7.5 - Evaluate the integral. 52. dxxx4+1 Ch. 7.5 - Prob. 61E Ch. 7.5 - Prob. 62E Ch. 7.5 - Evaluate the integral. 55. dxx+xx Ch. 7.5 - Evaluate the integral. 56. dxx+xx Ch. 7.5 - Prob. 65E Ch. 7.5 - Prob. 66E Ch. 7.5 - Prob. 67E Ch. 7.5 - Prob. 68E Ch. 7.5 - Evaluate the integral. 61. d1+cos Ch. 7.5 - Prob. 70E Ch. 7.5 - Prob. 71E Ch. 7.5 - Prob. 72E Ch. 7.5 - Prob. 73E Ch. 7.5 - Prob. 74E Ch. 7.5 - Prob. 75E Ch. 7.5 - Prob. 76E Ch. 7.5 - Evaluate the integral. 69. 131+x2x2dx Ch. 7.5 - Evaluate the integral. 70. 11+2exexdx Ch. 7.5 - Evaluate the integral. 71. e2x1+exdx Ch. 7.5 - Prob. 80E Ch. 7.5 - Evaluate the integral. 73. x+arcsinx1x2dx Ch. 7.5 - Prob. 82E Ch. 7.5 - Prob. 83E Ch. 7.5 - Prob. 84E Ch. 7.5 - Prob. 85E Ch. 7.5 - Evaluate the integral. 78. 1+sinx1sinxdx Ch. 7.5 - Prob. 87E Ch. 7.5 - Prob. 88E Ch. 7.5 - Prob. 89E Ch. 7.5 - Prob. 90E Ch. 7.5 - Prob. 91E Ch. 7.5 - Prob. 92E Ch. 7.5 - Prob. 93E Ch. 7.5 - Prob. 94E Ch. 7.5 - Prob. 95E Ch. 7.6 - Prob. 1E Ch. 7.6 - Prob. 2E Ch. 7.6 - Prob. 3E Ch. 7.6 - Use the formula in the indicated entry of the...Ch. 7.6 - Prob. 5E Ch. 7.6 - Prob. 6E Ch. 7.6 - Prob. 7E Ch. 7.6 - Prob. 8E Ch. 7.6 - Prob. 9E Ch. 7.6 - Prob. 10E Ch. 7.6 - Prob. 11E Ch. 7.6 - Prob. 12E Ch. 7.6 - Prob. 13E Ch. 7.6 - Prob. 14E Ch. 7.6 - Prob. 15E Ch. 7.6 - Prob. 16E Ch. 7.6 - Prob. 17E Ch. 7.6 - Prob. 18E Ch. 7.6 - Prob. 20E Ch. 7.6 - Prob. 21E Ch. 7.6 - Prob. 22E Ch. 7.6 - Prob. 23E Ch. 7.6 - Prob. 24E Ch. 7.6 - Prob. 25E Ch. 7.6 - Prob. 26E Ch. 7.6 - Prob. 27E Ch. 7.6 - Prob. 28E Ch. 7.6 - Prob. 29E Ch. 7.6 - Prob. 30E Ch. 7.6 - Prob. 31E Ch. 7.6 - Prob. 32E Ch. 7.6 - Prob. 33E Ch. 7.6 - Prob. 34E Ch. 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. 7E Ch. 7.7 - Prob. 8E Ch. 7.7 - Prob. 9E Ch. 7.7 - Prob. 11E Ch. 7.7 - Prob. 12E Ch. 7.7 - Prob. 13E Ch. 7.7 - Prob. 15E Ch. 7.7 - Prob. 16E Ch. 7.7 - Prob. 17E Ch. 7.7 - Prob. 18E Ch. 7.7 - Prob. 26E Ch. 7.7 - Prob. 29E Ch. 7.7 - Prob. 30E Ch. 7.7 - Prob. 31E Ch. 7.7 - Prob. 32E Ch. 7.7 - Prob. 33E Ch. 7.7 - Prob. 34E Ch. 7.7 - Prob. 35E Ch. 7.7 - Prob. 36E Ch. 7.7 - Prob. 37E Ch. 7.7 - Prob. 38E Ch. 7.7 - Prob. 39E Ch. 7.7 - Prob. 40E Ch. 7.7 - Prob. 41E Ch. 7.7 - Prob. 42E Ch. 7.7 - Prob. 43E Ch. 7.7 - Prob. 44E Ch. 7.8 - Find the area under the curve y = 1/x3 from x = 1...Ch. 7.8 - Prob. 4E Ch. 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. 8E Ch. 7.8 - Determine whether the integral is convergent or...Ch. 7.8 - Prob. 10E 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 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. 50E 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 - Sketch the region and find its area (if the area...Ch. 7.8 - Prob. 55E Ch. 7.8 - Prob. 56E Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Prob. 59E Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Use the Comparison Theorem to determine whether...Ch. 7.8 - Prob. 62E Ch. 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. 66E Ch. 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. 73E Ch. 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. 76E Ch. 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. 85E Ch. 7.8 - Prob. 86E Ch. 7.8 - Prob. 87E Ch. 7.8 - Prob. 88E Ch. 7.8 - Show that 0x2ex2dx=120ex2dx.Ch. 7.8 - Prob. 90E Ch. 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. 4CC Ch. 7 - Prob. 5CC Ch. 7 - Prob. 6CC Ch. 7 - Define the improper integral abf(x)dx for each of...Ch. 7 - State the Comparison Theorem for improper...Ch. 7 - Prob. 1TFQ Ch. 7 - Determine whether the statement is true or false....Ch. 7 - Prob. 3TFQ Ch. 7 - Prob. 4TFQ Ch. 7 - Determine whether the statement is true or false....Ch. 7 - Prob. 6TFQ Ch. 7 - Prob. 7TFQ Ch. 7 - Prob. 8TFQ Ch. 7 - Prob. 9TFQ Ch. 7 - Prob. 10TFQ Ch. 7 - Prob. 11TFQ Ch. 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. 15TFQ Ch. 7 - Prob. 16TFQ Ch. 7 - Determine whether the statement is true or false....Ch. 7 - Prob. 18TFQ Ch. 7 - Evaluate the integral. 1. 12(x+1)2xdx Ch. 7 - Evaluate the integral. 2. 12x(x+1)2dx Ch. 7 - Prob. 3E Ch. 7 - Prob. 4E Ch. 7 - Evaluate the integral. 5. dt2t2+3t+1 Ch. 7 - Evaluate the integral. 6. 12x5lnxdx Ch. 7 - Prob. 7E Ch. 7 - Prob. 8E Ch. 7 - Prob. 9E Ch. 7 - Prob. 10E Ch. 7 - Prob. 11E Ch. 7 - Prob. 12E Ch. 7 - Evaluate the integral. 11. 12x21xdx Ch. 7 - Prob. 14E Ch. 7 - Evaluate the integral. 13. ex3dx Ch. 7 - Prob. 16E Ch. 7 - Prob. 17E Ch. 7 - Prob. 18E Ch. 7 - Evaluate the integral. 15. x1x2+2xdx Ch. 7 - Prob. 20E Ch. 7 - Prob. 21E Ch. 7 - Prob. 22E Ch. 7 - Prob. 23E Ch. 7 - Prob. 24E Ch. 7 - Evaluate the integral. 19. x+19x2+6x+5dx Ch. 7 - Prob. 26E Ch. 7 - Prob. 27E Ch. 7 - Prob. 28E Ch. 7 - Prob. 29E Ch. 7 - Prob. 30E Ch. 7 - Prob. 31E Ch. 7 - Prob. 32E Ch. 7 - Prob. 33E Ch. 7 - Prob. 34E Ch. 7 - Prob. 35E Ch. 7 - Prob. 36E Ch. 7 - Prob. 37E Ch. 7 - Prob. 38E Ch. 7 - Prob. 39E Ch. 7 - Evaluate the integral. 32. 0/4xsinxcos3xdx Ch. 7 - Evaluate the integral. 33. x2(4x2)3/2dx Ch. 7 - Prob. 42E Ch. 7 - Prob. 43E Ch. 7 - Prob. 44E Ch. 7 - Prob. 45E Ch. 7 - Prob. 46E Ch. 7 - Prob. 47E Ch. 7 - Prob. 48E Ch. 7 - Prob. 49E Ch. 7 - Prob. 50E Ch. 7 - Prob. 51E Ch. 7 - Prob. 52E Ch. 7 - Prob. 53E Ch. 7 - Evaluate the integral or show that it is...Ch. 7 - Prob. 55E Ch. 7 - Prob. 56E Ch. 7 - Prob. 57E Ch. 7 - Prob. 58E Ch. 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. 62E Ch. 7 - Prob. 63E Ch. 7 - Prob. 64E Ch. 7 - Prob. 65E Ch. 7 - Prob. 66E Ch. 7 - Prob. 67E Ch. 7 - Prob. 68E Ch. 7 - Prob. 69E Ch. 7 - Prob. 70E Ch. 7 - Prob. 71E Ch. 7 - For what values of a is 0eaxcosxdx convergent?...Ch. 7 - Use (a) the Trapezoidal Rule, (b) the Midpoint...Ch. 7 - Prob. 74E Ch. 7 - Prob. 75E Ch. 7 - Prob. 76E Ch. 7 - Prob. 77E Ch. 7 - Prob. 78E Ch. 7 - Prob. 79E Ch. 7 - Prob. 80E Ch. 7 - Prob. 81E Ch. 7 - Prob. 82E Ch. 7 - Prob. 83E Ch. 7 - Prob. 84E Ch. 7 - The region under the curve y = cos2x, 0 x /2, is...Ch. 7 - Prob. 86E Ch. 7 - Prob. 87E Ch. 7 - Prob. 88E Ch. 7 - Prob. 89E Ch. 7 - Prob. 90E Ch. 7 - Prob. 1P Ch. 7 - Evaluate 1x7xdx The straightforward approach would...Ch. 7 - Prob. 3P Ch. 7 - Prob. 5P Ch. 7 - The centers of two disks with radius 1 are one...Ch. 7 - Prob. 7P Ch. 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. 12P Ch. 7 - If 0 a b, find limt0{01[bx+a(1x)]tdx}1/t Ch. 7 - Prob. 14P Ch. 7 - Prob. 15P Ch. 7 - Prob. 16P Ch. 7 - The circle with radius 1 shown in the figure...Ch. 7 - Prob. 18P

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