1. 7.2 Trigonometric Integrals Tues Jan 12 Do Now Evaluate

2. HW Review

3. Integrating Powers of Sine and Cosine 1) Determine which power is odd 2) Factor out one power of that trig 3) Use the trig identity to get rid of all powers of that trig except one 4) Use u-substitution on the OTHER trig function

4. Ex 3.2 sinx is odd Evaluate

5. Ex 3.3 cosx is odd Evaluate

6. Case 1: When tanx is odd 1) Factor out tanxsecx 2) Use the trig identity to remove all powers of trig (except 1) 3) Let u = secx (du = tanxsecx) 4) Integrate and replace u

7. Ex 3.6 Evaluate

8. Case 2: secx is even 1) Factor out one factor of 2) Use trig identity to replace remaining factors 3) Let u = tanx (du =) 4) Integrate and replace u

9. Ex 3.7 Evaluate

10. Other cases When we have a case where the substitution method does not work, we have several reduction formulas that can be found on p.410

11. Ex Evaluate

12. Ex Evaluate

13. Ex Evaluate

14. Closure If we use a reduction formula for an integral that could be evaluated by substitution, we would get 2 different (but equivalent) answers. Why? HW: p.411 #5 11 27 33 43 47 53 57 63 65