SEC 8.2: TRIGONOMETRIC INTEGRALS

1. SEC 8.2: TRIGONOMETRIC INTEGRALS Example Find Example Find

2. TRIGONOMETRIC INTEGRALS 1 1 2 2 to express the remaining factors in terms of cos to express the remaining factors in terms of sin

3. TRIGONOMETRIC INTEGRALS 1 sometimes helpful to use 2

4. TRIGONOMETRIC INTEGRALS Eliminating Square Roots we use the identity to eliminate a square root. Example Find

5. TRIGONOMETRIC INTEGRALS We can use a similar strategy to evaluate integrals of the form Example Find Example Find

6. TRIGONOMETRIC INTEGRALS 1 1 2 2 to express the remaining factors in terms of sec to express the remaining factors in terms of tan

7. EXAM-2 Term-082

8. TRIGONOMETRIC INTEGRALS the guidelines are not as clear-cut. We may need to use identities, integration by parts, and occasionally a little ingenuity.

9. TRIGONOMETRIC INTEGRALS the guidelines are not as clear-cut. We may need to use identities, integration by parts, and occasionally a little ingenuity. Example If an even power of tangent appears with an odd power of secant, it is helpful to express the integrand completely in terms of sec x Find Powers of sec x may require integration by parts, as shown in the following example.

10. TRIGONOMETRIC INTEGRALS Example Find

11. TRIGONOMETRIC INTEGRALS REMARK Integrals of the form can be found by similar methods because of the identity

12. 1 1 2 2 to express the remaining factors in terms of csc to express the remaining factors in terms of cot

13. EXAM-2 Term-122

14. Product of Sines and Cosines EXAM-2 Term-122

15. TRIGONOMETRIC INTEGRALS Powers of Sines and Cosines Products of Sines and Cosines TRIGONOMETRIC INTEGRALS Powers of tan x and sec x Eliminating Square Roots

16. EXAM-2 Term-092 EXAM-2 Term-092

17. TRIGONOMETRIC INTEGRALS function of tan and sec function of Sines and Cosines TRIGONOMETRIC INTEGRALS function of cot and csc EXAM-2 Term-092

18. EXAM-2 Term-092

19. EXAM-2 Term-092

20. EXAM-2 Term-092