求定积分:[(e的sinx次方)乘以cosx]dx,上限是2分之pai,下限是0?$(acontent)

问题描述:

求定积分:[(e的sinx次方)乘以cosx]dx,上限是2分之pai,下限是0?
$(acontent)

∫(0,π/2)[(e的sinx次方)乘以cosx]dx
=∫(0,π/2)[(e的sinx次方)dsinx
=e^(sinx)|(0,π/2)
=e-1

∫[0,π/2] e^(sinx ) cosxdx= ∫[0,π/2] e^(sinx ) dsinx= e^(sinx ) | [0,π/2] =e-1