MATH 182A Lecture 8: 7.2_trigonometric-integrals
Document Summary
Using concepts from trigonometric substitution, we can solve integrals with trigonometric functions by separating out even powers and using the following identities: sin2( ) + cos2( ) = 1. If we can isolate an even power of sin, we can substitute: sin2( ) = 1 cos2( ) If we can isolate an even power of cos, we can substitute: cos2( ) = 1 sin2( ) The same rules apply for even powers of tan, sec, cot, and csc. Z /2 (cos4(x) 2 cos2(x) + 1) sin(x)dx. Let : t = cos(x) dt = sin(x)dx. The limits from 0 to /2 become 1 to 0. (cid:18)r /2. We can ip the integral and negate it to remove the minus sign. Let : t = sec(x) dt = sec(x) tan(x)dx. Let : t = tan( ) dt = sec2( ) Z t2 + t6dt t5 + c t3 + If any errors are found, please contact me at alvin. lin. dev@gmail. com.
