Rules of integration

calculus

1. Rules of Integration Exponential and Trigonometric Function

2. ... finding an Integral is the  reverse  of finding a Derivative. (So you should really know about  Derivatives   ) Like here: Example: What is an integral of 2x? We know that the derivative of x 2  is 2x ... ... so an integral of 2x is x 2

3. Rules of Integration in Exponential Function 1. 2. 3.

4. Remember the three General rules for Integration 1. 2. 3.

5. Examples: Integrate 2. Integrate .

6. 3. Integrate u-substitution u = -x du = -1 dx -1 du = dx

7. Example: Integrate

8. Example: Integrate

9. Examples: Integrate

10. Examples: Integrate u-substitution u = 2x+3 du = 2 dx (1/2) du = dx

11. Rules of Integration in Trigonometric Function

12. Trigonometric Functions A. B. C. D. C . D . E. F . G. H. I.

13. Rules of Differentiation

14. Indefinite Integrals

15. Indefinite integrals result from trigonometric identities and u-substitution

16. Examples A. Integrate u-substitution u = 3x du = 3dx (1/3) du = dx Recall

17. B. Integrate Examples u-substitution u = 5x du = 5dx (1/5) du = dx Recall

18. C. Integrate Examples u-substitution u = 4x du = 4dx (1/4) du = dx Recall

19. D. Integrate Examples

20. Trigonometric Functions A. B. C. D. C . D . E. F . G. H. I.

21. D. Integrate Examples

22. Indefinite Integrals

23. D. Integrate Examples u-substitution u = sin x du = cos x dx

24. Rules of Differentiation

25. D. Integrate Examples u-substitution u = sin x du = cos x dx

26. E. Integrate Examples

27. Trigonometric Functions A. B. C. D. C . D . E. F . G. H. I.

28. E. Integrate Examples u-substitution u = 10x du = 10dx (1/10)du = dx

29. F . Integrate Example u-substitution u = sin x du = cos dx Recall

30. INTEGRATE THE FOLLOWING 1. u-substitution u-substitution

31. Thank You and God Bless