Integral with trigonometric functions

CONCEPT

ATOQ

1. What is the integral of \sin x?
A) \cos x
B) -\cos x
C) \sin x
D) -\sin x

2. What is the integral of \cos x?
A) \sin x
B) -\sin x
C) \cos x
D) -\cos x

3. What is the integral of \sec^2 x?
A) \sin x
B) \tan x
C) \sec x
D) -\tan x

4. What is the integral of \sin^2 x?
A) \frac{x}{2} - \frac{\sin 2x}{4}
B) \frac{x}{2} + \frac{\sin 2x}{4}
C) \frac{x}{2} - \frac{\cos 2x}{4}
D) \frac{x}{2} + \frac{\cos 2x}{4}

5. What is the integral of \cot x?
A) \ln |\sin x|
B) -\ln |\sin x|
C) \ln |\cos x|
D) -\ln |\cos x|

6. What is the integral of \csc^2 x?
A) \cot x
B) -\cot x
C) \csc x
D) -\csc x

7. What is the integral of \sec x \tan x?
A) \sec x
B) -\sec x
C) \tan x
D) -\tan x

8. What is the integral of \tan^2 x?
A) \tan x - x
B) \sec^2 x - x
C) \tan x + x
D) \sec^2 x + x

9. What is the integral of \sec x \sec \tan x?
A) \ln |\sec x + \tan x|
B) \ln |\sec x - \tan x|
C) -\ln |\sec x + \tan x|
D) -\ln |\sec x - \tan x|

10. What is the integral of \frac{1}{\sin x}?
A) \ln |\csc x + \cot x|
B) -\ln |\csc x + \cot x|
C) \ln |\csc x - \cot x|
D) -\ln |\csc x - \cot x|

11. What is the integral of \cos^2 x?
A) \frac{x}{2} + \frac{\sin 2x}{4}
B) \frac{x}{2} - \frac{\sin 2x}{4}
C) \frac{x}{2} + \frac{\cos 2x}{4}
D) \frac{x}{2} - \frac{\cos 2x}{4}

12. What is the integral of \sin x \cos x?
A) \frac{1}{2}\sin^2 x
B) \frac{1}{2}\cos^2 x
C) \frac{1}{2}\sin 2x
D) \frac{1}{2}\cos 2x

13. What is the integral of \frac{1}{\cos x}?
A) \ln |\sec x + \tan x|
B) \ln |\sec x - \tan x|
C) -\ln |\sec x + \tan x|
D) -\ln |\sec x - \tan x|

14. What is the integral of \frac{\sin x}{\cos^2 x}?
A) \ln |\cos x|
B) -\ln |\cos x|
C) \sec x
D) -\sec x

15. What is the integral of \tan x \sec^2 x?
A) \frac{\tan^2 x}{2}
B) \frac{\sec^2 x}{2}
C) \tan^3 x
D) \sec^2 x

16. What is the integral of \csc x \cot x?
A) \csc x
B) -\csc x
C) \cot x
D) -\cot x

17. What is the integral of \sin 2x?
A) -\frac{1}{2}\cos 2x
B) \frac{1}{2}\cos 2x
C) \frac{1}{2}\sin 2x
D) \frac{1}{2}\sin x

18. What is the integral of \frac{\sin^2 x}{\cos x}?
A) \tan x - \sin x
B) \tan x + \sin x
C) \sec x - \sin x
D) \sec x + \sin x

19. What is the integral of \frac{1}{\sin^2 x}?
A) \cot x
B) -\cot x
C) \csc x
D) -\csc x

20. What is the integral of \cos x \sin x?
A) \frac{1}{2}\sin^2 x
B) \frac{1}{2}\cos^2 x
C) \frac{1}{2}\sin 2x
D) \frac{1}{2}\cos 2x

KEY

1. B) -\cos x
2. A) \sin x
3. B) \tan x
4. B) \frac{x}{2} + \frac{\sin 2x}{4}
5. B) -\ln |\sin x|
6. B) -\cot x
7. A) \sec x
8. B) \sec^2 x - x
9. A) \ln |\sec x + \tan x|
10. A) \ln |\csc x + \cot x|
11. D) \frac{x}{2} - \frac{\cos 2x}{4}
12. C) \frac{1}{2}\sin 2x
13. A) \ln |\sec x + \tan x|
14. B) -\ln |\cos x|
15. C) \tan^3 x
16. B) -\csc x
17. A) -\frac{1}{2}\cos 2x
18. A) \tan x - \sin x
19. B) -\cot x
20. C) \frac{1}{2}\sin 2x