help please 6.3, do ex 1, 3, 5, 9, 10, 12, 15, 17, 19, 35

6.5 ex( 7a, 7c, 17 (T₈ refers to the trapezoidal rule with n=8. Do not worry about the part of this problem that applies to the midpoint rule), 18 (same instructions), 19 (again ignore the midpoint rule)

334 CHAPTER 6 TECHNIQUES OF INTEGRATION which has the solution A = 1, B = -1, C = -1, D = 1, and E = 0. Thus * (x2 + 1 ) 2 (1 - x + 2x -* dx - (x - 72 + 1 + (x 2 + 1)? ) d In the second and fourth terms we - In |x| - { In(x2 + 1) - tan 'x - 1 - + K made the mental substitution u = x2 + 1. 2 ( x 2 + 1 ) ' 6.3 EXERCISES 1-6 - Write out the form of the partial fraction decomposition of x2 + 1 x - 5x + 16 the function (as in Example 6). Do not determine the numerical 19. ) ( x - 3) (x - 2 )2 dx 20. J (2x + 1) (x - 2)2 dx values of the coefficients. 1 + 6x 10 1. (a) (4x - 3)(2x + 5) (b ) 21. ( x + 4 dx 22. 5x2- 2x3 x2 + 4 x3 + 3x 10 x2 - 2x - 1 2. (a) -2 x2 + x - 2 (b) xtx+2 23. J ( x - 1)(x2 + 9) dx 24. ( x - 1) ?(x2 + 1 ) - dx x'+ 1 3. (a) ( + x2 + 2x + 1 dx x - 2x + x + 1 dx x5 + 4x3 ( b ) (x2 - 9)2 25. J ( x2 + 1 )(x2 + 2) 26. * 4 + 5x2 + 4 4. (a) x- 2x3 + x2+ 2x -1 x+ 4 x2 - 2x + 1 (b ) x3 + x 2 + x 27. x2 + 2x + 5' 28. Jo x2 + 4x + 13 dx 5. (a)- (x2 - x + 1)(x2+ 2)2 29. 73 - 1 x + x - 1 x2 - 4 ( b ) 30.3+ 1 - dx 10 + 1 x' + 1 6. (a)- dx x + 3x2 + 1 16 + 1 3 (6) ( x2 - x)(x* + 2x2 + 1) 31. x(x 2 + 4) 2 32. x5 + 5x3+ 5x -dx x - 3 7-34 . Evaluate the integral. 33. ( x 2 + 2x + 4)2 dx 34. x +1 x (x2 + 1)2 dx 7.dx 31 - 2 di 8. 7+ 1 35-40 . Make a substitution to express the integrand as a 5x + 1 dx 10. J ( y + 4)(2y - 1) y rational function and then evaluate the integral. 9. ) (2x + 1)(x - 1) 35. [16 * dx ( Let u = Vx.) 2 x - 4 11. Jo 2x2 + 3x + 1 dx 12. Jo x2 - 5x + 6 dx 36. Jo + 1/ dx (Let u = Vx.) 13. dx x2 - bx 14 . ) ( x + a ) ( x + b ) dx dx 15. (1 2x + 3 x3 - 4x - 10 dx 37. x2 + 1 38. xat x ( x + 1 )2 dx 16. 10 x2 - x - 6 e 2x 4y2 - 7y - 12 x2 + 2x - 1 39. 2x + 3e* + 2 - dx 40. sin x - dx 17. J, ( y + 2)(y -3) - dy 18. cos x - 3 cos x x3 - x - dx Unless otherwise noted, all content on this page is @ Cengage Learning7-16 - Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) 2 7. Vx3 - 1 dx, n = 10 8. I + 6 ax, n = 817. (a) Find the approximations 7: and Mg for the integral So cos(x2) dx. (b) Estimate the errors in the approximations of part (a). (c) How large do we have to choose n so that the approxi- mations T, and M, to the integral in part (a) are accu- rate to within 0.0001? 18. (a) Find the approximations Tio and Mio for f? el/* dx. (b) Estimate the errors involved in the approximations of part (a). (c) How large do we have to choose n so that the approxi- mations T, and M, to the integral in part (a) are accu- rate to within 0.0001? 19. (a) Find the approximations 710, M10, and Sio for " sin x dx and the corresponding errors Er, EM, and Es. (b) Compare the actual errors in part (a) with the error estimates given by 3 and 4. (c) How large do we have to choose n so that the approxi- mations T,, M., and S,, to the integral in part (a) are accurate to within 0.00001