# BC Calculus : MC Integration Practice

• Class: 5H: BC Calculus
• Author: Peter Atlas
• Text: Calculus Finney, Demana, Waits, Kennedy

1. $$\displaystyle \int_{-1}^{1} (x^2 - x - 1) \, dx =$$
1. $$\frac{2}{3}$$
2. 0
3. $$-\frac{4}{3}$$
4. -2
5. -1
2. Solution C
3. $$\displaystyle \int_{1}^{2} \frac{3x - 1}{3x} \, dx =$$
1. $$\frac{3}{4}$$
2. $$1 - \frac{1}{3}\ln{2}$$
3. $$1 - \ln{ 2}$$
4. -$$\frac{1}{3}\ln{ 2}$$
5. 1
4. Solution B
5. $$\displaystyle \int_{0}^{3} \frac{dt}{\sqrt{4 - t}} =$$
1. 1
2. -2
3. 4
4. -1
5. 2
6. Solution E
7. $$\displaystyle \int_{-1}^{0} \sqrt{3u + 4} \, du =$$
1. 2
2. $$\frac{14}{9}$$
3. $$\frac{4}{3}$$
4. 6
5. $$\frac{7}{2}$$
8. Solution B
9. $$\displaystyle \int_{2}^{3} \frac{dy}{2y - 3} =$$
1. $$\ln{ 3}$$
2. $$\frac{1}{2} \ln{ \left( \frac{3}{2} \right) }$$
3. $$\frac{16}{9}$$
4. $$\frac{1}{2}\ln{3}$$
5. $$\sqrt{3} - 1$$
10. Solution D
11. $$\displaystyle \int_{0}^{\sqrt{3}} \frac{x dx}{ \sqrt{4 - x^2}} =$$
1. 1
2. $$\frac{\pi }{6}$$
3. $$\frac{ \pi}{3}$$
4. -1
5. 2
12. Solution A
13. $$\displaystyle \int_{0}^{1} (2t - 1)^3 \, dt =$$
1. \frac{1}{4}
2. 6
3. $$\frac{1}{2}$$
4. 0
5. 4
14. Solution D
15. $$\displaystyle \int_{0}^{1} \frac{dx}{\sqrt{4 - x^2}} =$$
1. $$\frac{ \pi}{3}$$
2. $$2 -\sqrt{3}$$
3. $$\frac{ \pi}{12}$$
4. $$2( \sqrt{3} - 2)$$
5. $$\frac{\pi }{6}$$
16. Solution E
17. $$\displaystyle \int_{4}^{9} \frac{(2 + x) dx}{2 \sqrt{x}} =$$
1. $$\frac{25}{3}$$
2. $$\frac{41}{3}$$
3. $$\frac{100}{3}$$
4. $$\frac{5}{3}$$
5. $$\frac{1}{3}$$
18. Solution A
19. $$\displaystyle \int_{-3}^{3} \frac{dx}{9 + x^2} =$$
1. $$\frac{ \pi}{2}$$
2. 0
3. $$\frac{\pi }{6}$$
4. $$- \frac{ \pi}{2}$$
5. $$\frac{ \pi}{3}$$
20. Solution C
21. $$\displaystyle \int_{0}^{1}e^{-x} \, dx =$$
1. $$\frac{1}{e} - 1$$
2. $$1 - e$$
3. $$- \frac{1}{e}$$
4. $$1 - \frac{1}{e}$$
5. $$\frac{1}{e}$$
22. Solution D
23. $$\displaystyle \int_{0}^{1} xe^{x^2} \, dx =$$
1. $$e - 1$$
2. $$\frac{1}{2}(e - 1)$$
3. $$2(e - 1)$$
4. $$\frac{e}{2}$$
5. $$\frac{e}{2} - 1$$
24. Solution B
25. $$\displaystyle \int_{0}^{ \frac{ \pi}{4} }\sin{(2\theta )} \, d\theta =$$
1. 2
2. $$\frac{1}{2}$$
3. -1
4. $$-\frac{1}{2}$$
5. -2
26. Solution B
27. $$\displaystyle \int_{1}^{2} \frac{dz}{3 - z} =$$
1. $$-\ln{2}$$
2. $$\frac{3}{4}$$
3. $$2(\sqrt{2} - 1)$$
4. $$\frac{1}{2}\ln{ 2}$$
5. $$\ln{ 2}$$
28. Solution E
29. $$\displaystyle \int_{1}^{e} \ln{ y} \, dy =$$
1. $$2e + 1$$
2. $$\frac{1}{2}$$
3. 1
4. $$e - 1$$
5. -1
30. Solution C
31. $$\displaystyle \int_{-4}^{4} \sqrt{16 - x^2} \, dx =$$
1. $$8 \pi$$
2. $$4 \pi$$
3. 4
4. 8
5. none of these
32. Solution A
33. $$\displaystyle \int_{0}^{ \pi } \cos^2{\theta }\sin{ \theta } \, d\theta =$$
1. $$-\frac{2}{3}$$
2. $$\frac{1}{3}$$
3. 1
4. $$\frac{2}{3}$$
5. 0
34. Solution D
35. $$\displaystyle \int_{1}^{e} \frac{\ln{ x}}{ x} \, dx =$$
1. $$\frac{1}{2}$$
2. $$\frac{1}{2}(e^2 - 1)$$
3. 0
4. 1
5. $$e - 1$$
36. Solution A
37. $$\displaystyle \int_{0}^{1} xe^x \, dx =$$
1. -1
2. $$e + 1$$
3. 1
4. $$e - 1$$
5. $$\frac{1}{2}(e - 1)$$
38. Solution C
39. $$\displaystyle \int_{0}^{ \frac{\pi }{6}} \frac{\cos {\theta } }{1 + 2 \sin {\theta}} \, d\theta =$$
1. $$\ln{ 2}$$
2. $$\frac{3}{8}$$
3. $$-\frac{1}{2}\ln{ 2}$$
4. $$\frac{3}{2}$$
5. $$\ln{ \sqrt{2}}$$
40. Solution E
41. $$\displaystyle \int_{\sqrt{2}}^{2} \frac{u}{u^2 - 1} \, du =$$
1. $$\ln{ \sqrt{3}}$$
2. $$\frac{8}{9}$$
3. $$\ln{ \frac{3}{2}}$$
4. $$\ln{ 3}$$
5. $$1 - \sqrt{3}$$
42. Solution A
43. $$\displaystyle \int_{\sqrt{2}}^{2} \frac{u}{(u^2 - 1)^2} \, du =$$
1. $$-\frac{1}{3}$$
2. $$-\frac{2}{3}$$
3. $$\frac{2}{3}$$
4. -1
5. $$\frac{1}{3}$$
44. Solution E
45. $$\displaystyle \int_{ \frac{ \pi}{12}}^{ \frac{ \pi}{4}} \frac{\cos {(2x)} }{\sin^2 {(2x)}} =$$
1. $$-\frac{1}{4}$$
2. 1
3. $$\frac{1}{2}$$
4. $$-\frac{1}{2}$$
5. -1
46. Solution C
47. $$\displaystyle \int_{0}^{1} \frac{e^{-x} + 1}{ e^{-x}} \, dx =$$
1. $$e$$
2. $$2 + e$$
3. $$\frac{1}{e}$$
4. $$1 + e$$
5. $$e - 1$$
48. Solution A
49. $$\displaystyle \int_{0}^{1} \frac{ e^x dx}{e^x + 1} =$$
1. $$\ln{ 2}$$
2. $$e$$
3. $$1 + e$$
4. $$-\ln{ 2|}$$
5. $$\ln{ \left( \frac{e + 1}{2} \right) }$$
50. Solution E
51. If the substitution $$u = \sqrt{x + 1}$$ is used, then $$\displaystyle \int_{0}^{3} \frac{dx}{x\sqrt{x + 1}}$$ is equivalent to
1. $$\displaystyle \int_{1}^{2} \frac{du}{u^2 - 1}$$
2. $$\displaystyle \int_{1}^{2} \frac{2du}{u^2 - 1}$$
3. $$2 \displaystyle \int_{0}^{3} \frac{du}{(u - 1)(u + 1)}$$
4. $$2 \displaystyle \int_{1}^{2} \frac{du}{u(u^2 - 1)}$$
5. $$2 \displaystyle \int_{0}^{3} \frac{du}{u(u - 1)}$$
52. Solution B