Final Daily Quiz of 1 st Quarter!!!!!!

1. Final Daily Quiz of 1st Quarter!!!!!! • 2. • 3.

2. Essential Question

3. Section 8.3 Trigonometric Integrals

5. Mastering today’s topic is all about having a logical problem solving strategy and recognizing patters! Pro-Tip: Don’t try to memorize…just think about your goal!

6. Example 1: (n Odd) Could you do this problem if the integral was a product of sine and cosine? Strategy: Factor out an even number of sin x and swap it for cos x (Pythagorean Identity). Then use u-substation to integrate. How would you go about integrating cosine to an odd power? Similarities/Differences?

7. Example 2: (n Even) Strategy: Power Reduction Formula How would you go about integrating sine to an even power? Similarities/Differences?

8. Example 3: ( m or n Odd) Could we get u-substitution to work for us? Strategy: Leave one sine/cosine and re-write the rest using the Pythagorean Identity. Then you can use u-substitution to integrate. If you have sinodd you re-write______. If you have cosodd you re-write______.

9. Example 4: ( m and n Even) Will our strategy from the previous slide work? Strategy: Use Power Reduction Identities on BOTH trig functions.

10. Example 5: Strategy: Product – Sum Formulas

11. Example 6: What trigonometric functions “is friends” with cotangent?

12. Example 7: What trigonometric functions “is friends” with tangent?

13. Example 8: Strategy: Basic u-substation…don’t rush to judgement and overcomplicate things!

14. Example 9: What trigonometric functions “is friends” with tangent? What trigonometric functions “is friends” with secant? Strategy: Create a situation when you can do a u-substitution with u = sec (x) and du=sec(x)tan(x).

15. Guidelines for Evaluating Integrals Involving Sine and Cosine

16. Guidelines for Evaluating Integrals Involving Secant and Tangent

17. Homework Section 8.3 #5-17 odds, 33-41 odds, 43, 51, 67, 95