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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 | | Español |
| | Answers to Odd-Numbered Exercises |
Calculate the following integrals
| 1. | $(\sin x - \cos x) dx $ | 2. | $(\tan x + \cos x) dx$ | 3. | $cosec(2x - 3) dx$ | |||
| 4. | $\tan(7x + 2) dx $ | 5. | $x cotan(x^2 - 1) dx$ | 6. | $(x+1)\cos(x^2 + 2x) dx$ | |||
| 7. | $\cos x \sin^3x dx$ | 8. | $\sin x \cos^4x dx$ | 9. | $cosec^2(2x - 3) dx$ | |||
| 10. | $\sec(2x - 3)\tan(2x - 3) dx$ | 11. | $x^{-2} \sin(1/x) dx$ | 12. | $\frac{\sin x}{1 + \cos x} dx$ | |||
| 13. | $\cos x(1 - \sin x) dx$ | 14. | $e^x + \sec^2 \frac{x}{e^x + \tan x} dx$ | 15. | $e^x \tan(e^x) dx$ | |||
| 16. | ∫ | $(x \cos x) dx$ | 17. | $(2x - 1)\sin x dx$ | 18. | $(x^2- x + 4)\sin(2x) dx$ | ||
| 19. | $(x^3\cos(x/2)) dx$ | 20. | $(e^{2x}\sin x) dx$ | 21. | $(e^{-x}\cos x) dx$ | |||
| 22. | $(\sin x)(\ln \|\cos x\|) dx$ | 23. | $(\cos x)(\ln \|\sin x\|) dx$ | 24. | $\tan^2x dx$ |
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. | $\sin^2x = 0.5(x - 0.5\sin(2x)) dx$ |
Calculate the following definite integrals
| 29. | ∫ | $π$ $0$ |
$\sin x dx$ | 30. | ∫ | $π$ $0$ |
$\cos x dx$ | 31. | ∫ | $π/4$ $0$ |
$\tan x dx$ |
| | 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) |