for
Section 4: Integrals of Trigonometric Functions
 | 3. Derivatives of Trigonometric Functions | | 4. Integrals of Trigonometric Functions | | Trigonometric Functions Main Page | | "RealWorld" Page | | Everything for Calculus |
| | Answers to Odd-Numbered Exercises |
Calculate the following integrals
| 1. |  |
(sin x  cos x) dx |
2. | |
(tan x + cos x) dx | 3. | |
cosec(2x3) dx |
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| 4. | |
tan(7x+2) dx | 5. | |
x cotan(x21) dx |
6. | |
(x+1)cos(x2+2x) dx | ||
| 7. | |
cos x sin3x dx | 8. | |
sin x cos4x dx | 9. | |
cosec2(2x3) dx |
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| 10. | |
sec(2x3)tan(2x3) dx |
11. | |
x 2sin(1/x) dx |
12. | |
|
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| 13. | |
cos x(1 sin x) dx |
14. | |
|
15. | |
extan(ex) dx | ||
| 16. | |
(x cos x) dx | 17. | |
(2x1)sin x dx |
18. | |
(x2x+4)sin(2x) dx |
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| 19. | |
(x3cos(x/2)) dx | 20. | |
(e2xsin x) dx | 21. | |
(excos x) dx |
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| 22. | |
(sin x)(ln |cos x|) dx | 23. | |
(cos x)(ln |sin x|) dx | 24. | |
tan2x dx |
Verify the following integrals either by computing the integral directly, or by differentiating the answer.
| 25. | |
cotan x dx = ln |sin x| + C | 26. | |
sec x dx = ln |sec x + tan x| + C |
| 27. | |
cosec x dx = ln |cosec x + cotan x| + C |
28. | |
sin2x = 0.5(x0.5sin(2x)) dx |
Calculate the following definite integrals
| 29. | |  0 |
sin x dx | 30. | | 0 |
cos x dx | 31. | | /4 0 |
tan x dx |
| | 3. Derivatives of Trigonometric Functions | | 4. Integrals of Trigonometric Functions | | Trigonometric Functions Main Page | | "RealWorld" Page | | Everything for Calculus |
| | Answers to Odd-Numbered Exercises |
 | Stefan Waner (matszw@hofstra.edu) | | Steven R. Costenoble (matsrc@hofstra.edu) |
