Math 187 Practice Test 3

Math 187Practice Questions for Test 31. Evaluate ∫x cos(2x) dxAnswer: x 2 sin(2x) + 1 4 cos(2x) + C2. Evaluate ∫Answer: ln ∣√4+x 2 +x2∣ + Cdx√4 + x23. Evaluate ∫x 4 ln x dxAnswer: x55 ln x − 1 25 x5 + C4. Evaluate ∫Answer: − 1 3 ln ∣ ∣∣ 3x + √ 9−x 2x∣ + Cdxx √ 9 − x 25. Evaluate ∫x 2 e 3x dx()Answer: e 3x x 23 − 2x 9 + 2 27+ C6. Evaluate ∫Answer: ( ) 12 tan−1 x+32 + C7. Evaluate ∫Answer: sin −1 ( )ln t2 + Cdxx 2 + 6x + 13dtt √ 4 − (ln t) 28. Evaluate ∫ √4 − x2dxAnswer: − √ 4−x 2x− sin −1 ( x2)+ C9. Evaluate ∫e x cos x dxAnswer: ex 2(cos x + sin x) + Cx 210. Evaluate ∫ 2x 3 − 3x 2 − 3x − 10x 2 − 2x − 3Answer: x 2 + x + 3 ln |x + 1| + 2 ln |x − 3| + Cdx

Math 187 Practice Questions for Test 3 Page 2 of 211. Evaluate ∫Answer: − 1 3 ln |x − 1| + ln |x − 3| + 1 3ln |x + 2| + C12. Evaluate ∫Answer: 1 2 ln ∣ x+3∣ x+1 −3x+3 + Cx 2 + 1(x − 1)(x − 3)(x + 2) dx2x(x + 1)(x + 3) 2 dx13. Evaluate ∫ 3x 2 + x + 8x 3 + 4xAnswer: 2 ln |x| + 1 2 ln(x2 + 4) + 1 2 tan−1 ( x2)+ C14. Evaluate ∫Answer: 1 4 ln ∣ ∣ xx+2(∣ +1 12 x+2)+ Cdxx(x + 2) 215. Find all the first partial derivatives of z = x 3 y + sin(xy) + x 2 y 3 + 3y 4 .Answer: ∂z∂x = 3x2 y + y cos(xy) + 2xy 3 and ∂z∂y = x3 + x cos(xy) + 3x 2 y 2 + 12y 316. Evaluate f x (1, 2) and f y (1, 2) for f(x, y) = x 3 y + 3y 2 x + x 4 .Answer: f x (1, 2) = 22 and f y (1, 2) = 13.dx17. Evaluate ∫ 20Answer: 56∫ 3(x 3 y + 2x) dx dy118. Evaluate ∫ 10Answer: 2/5∫ 2x0x 2 y dy dx19. Find the first-octant volume under the plane x + y + z = 4.Answer: 32/320. Find the volume above the xy-plane and under the surface z = 4 − x 2 − y 2 .Answer: 8π21. Find the first-octant volume bounded by the xy-plane, the planes x = y, y = 2, and z = 2 + x 2 + y 2 .Answer: 28/322. Find the first-octant volume under the plane z = x + y and inside the cylinder x 2 + y 2 = 9.Answer: 18