Integrating Products of sine and cosine Let m and n be integers. Evaluate § sin-x cos" x dr. Strategy The power of cosine is odd n=2k +1 >0 Isin" x cos" x dr-/sin-x(cos x)' cos x dx in-in x) cos.a de Strategy The power of sine is odd ,n = 2k+1>0 jsin" xcos' x ds-(sin' x) cos" rsin.x d (1-cos) cos" xsin a d -10-112)' u" du If the powers of both sine and cosine are odd, both Strategies can be used. Strategy 3-2 The powers of both sine and cosine are even n= 2k 20 and m = 21120 sin" xcos"r dr = (sin, x)', (cos, x)' dc (1-cos 2x ) (1+cos 2x Foil out and use Strategy C-O and C-E
