计算定积分:∫cosx(1+sinx)dx,(区间0到π/2 )
问题描述：
计算定积分:∫cosx(1+sinx)dx,(区间0到π/2 )
答
=∫cosxdx+∫sinxcosxdx
=sinx+(1/2)∫sin2xdx
=sin(π/2)-sin0+(1/4)∫sin2xd2x
=1-(1/4)cos2x
=1-(1/4)(cosπ-cos0)
=1+1/2
=1.5