求定积分∫π0 esin x cos xdx

题目

求定积分∫π0 esin x cos xdx

答案

∫(0,π)e^(sin x) *cos xdx
=∫(0,π)e^(sin x) *dsinx
=e^(sin x)|(0,π)
=e^0-e^0
=1-1
=0