用定积分换元法计算0-派/2 sinx(cosx)^3dx

题目

用定积分换元法计算0-派/2 sinx(cosx)^3dx

答案

∫0-派/2 sinx(cosx)^3dx
=-∫(0,π/2)(cosx)^3dcosx
=-1/4 (cosx)^4|(0,π/2)
=-1/4 [(cosπ/2)^4-(cosπ/2)^4]
=-1/4(0-1)
=1/4