7.2 Trigonometric Integrals Tues Jan 12 Do Now Evaluate

HW Review

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

Ex 3.2 sinx is odd Evaluate

Ex 3.3 cosx is odd Evaluate

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

Ex 3.6 Evaluate

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

Ex 3.7 Evaluate

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

Ex Evaluate

Ex Evaluate

Ex Evaluate

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 #