1. (1 point) 6. (1 point) Evaluate the indefinite integral: ju NOTE REGARDING MA103 HOMEWORK SET 10: ?n/! 343x2 cos(7x) dx =. THE PROBLEMS IN THIS ASSIGNMENT MAY IN- VOLVE THE USE OF THE SUBSTITUTION RULE (5.5 NOTE: Don't forget the constant of integration. IN TEXT), INTEGRATION BY PARTS (7.1), PARTIAL FRACTION EXPANSION (7.4), OR A COMBINATION 7. (1 point) OF THE TECHNIQUES. AS ALWAYS, IT IS HIGHLY Evaluate the indefinite integral: RECOMMENDED THAT YOU ATTEMPT THE AS- SIGNED PROBLEMS FROM THE TEXT BEFORE TRY- ex cos (4x) dx = ING THESE PROBLEMS. NOTE: Don't forget the constant of integration. Evaluate the indefinite integral: 8. (1 point) Given that Q(x) = (x -1)'(x2+1)3 (x2 - 1)2, xe -2 dx = O(x) has: NOTE: Don't forget the constant of integration. (a) - single irreducible linear factors. 2. (1 point) Evaluate the indefinite integral (b) - repeated irreducible linear factors. (c ) single irreducible quadratic factors. becos(x) sin(x) dx =. (d) repeated irreducible quadratic factors. 9. (1 point) NOTE: Don't forget your constant of integration. What is the correct form of the partial fraction decomposi- tion for the following integral? 3. (1 point) Evaluate the indefinite integral: 7 (x8 + 3) xsin(-1x) dx = (x - 4) (12 - 1)2 (12 + 4) 2 dx . A. There is no partial fraction decomposition because NOTE: Don't forget the constant of integration. the denominator does not factor. Bx + C Dx + E . B. / x- 4+ (x2 - 1)2 + (x2 + 4)2) dx 4. (1 point) Evaluate the indefinite integral: . C. / A B C x - 4+ ( x2 - 1) 2 + ( x 2 + 4) 2 dx Inx 3 dx =. . D. There is no partial fraction decomposition yet be- cause there is cancellation. B "c D E Fx+ G NOTE: Don't forget the constant of integration. . E. (x-4+ x+ 17 ( x + 1 )2 + x x-1 (x- 1)27 x2 +4 Bx + C Cx + D Ex +F Gx + H 5. (1 point) . F. A (x-4+ 72 - 1+ ( x2 -1)2 7 x2+4 (x2+4)2 dx Evaluate the definite integral: . G. There is no partial fraction decomposition yet be- cause long division must be done first. dx xvinx . H./4 B C D E x - Atx+1 (x +1 ) 2 Fx+ G x- 17 ( x-1)2 x2 + 410. (1 point) Consider the definite integral: 14. (1 point) Evaluate the indefinite integral: x + 76 x2 + 6x +8 dx = 10x x2 + 5x +6 -dx NOTE: Don't forget the constant of integration. 15. (1 point) Consider the indefinite integral: Determine the numerical values of A and B, where B