integration

2. Using integration by parts (IBP), what should you pick for u and du in / 5x cos(3x) dx? A. u = cos(3x), du = 5x dx B. u = 5x, du = cos(3x) d.x C. u = cos(3.x), du = 5 dx D. u =5, du = x cos(3x) dx E. none of the above 3. What approach of integration by parts does solving / et cos(x) dax involve? A. separating B. cycling C. multiplying D. crying @ E. none of the above8. Which of the [allowing integrals can NOT be computed using the methods we have (towered so far? I./3:r:"2 (1:1: H./3:2rz"dr HI./rr"2 (tr IV./;r(:()s(:r2)r:r 1/1/12 (30501:) rim [3. [I C. 111 I). IV ILL V F. None of them For the following problems, match the methorl that works the best {that can he used to compute the integral, and is the best option) to compute the given integral. (Note: you do not need to compute the integrals to answer this question). Use these choices: A. U-Substitution B. Integration By Parts C. 'ITigonomctric Powers D. N one of these techniques work. 9. fsin'r'[:r)cos3[:r)d:r 10. f 6' d2: 5+6\": 11. fsin($2) d9: 12. [322 sin(:.r:3) d3: 13. [cos2(:r) (11: Never forget, we ALWAYS choose UiSubstitution whenever is possible. 47-2 dx, this integral would look like: 14. After the correct trigonometric substitution for V2- 72 7/4 8 sin (0) A. do V2 cos(0) 7 / 4 B. 8 sin?(0) de 7/2 4 sin (0) C. 0 V2 cos(0) TT / 4 D. 8 sec2 (0) do 0 E. None of the above15. Suppose you used the trigonometric substitution r = 3 tan 0 for an integral which involved v9 + x2 and you found the antiderivative to be -0 - 2 sec0 + cos0 + C. What is the final answer (in terms of a)? A. - tan 2v9+ x2 3 NIH + 3 + C V9+ 22 B. tan (x) + 2V9 + x2 3 + 3 + C V9 + 22 C. tan -1 V9 + x2 3 3 + V9 + 72 + C D. - tan (x) + 2V9+ x2 + 3 + C V9 + x2 E. None of the above\f18. Calculate the following integral: 7 (r - 3)(x + 4) A. In x - 3 +Inc+4+ C B. 4Inx- 3 +3 1=+4+ C C. 4In x - 3- 31+4 + C D. In - 3- In:+4 + C E. 3In x - 3 -41=+4+ C F. None of the above