∫(cosx)∧3dx,积分区域[-π╱2,π╱2]

问题描述:

∫(cosx)∧3dx,积分区域[-π╱2,π╱2]

原式=∫(cosx)^2*cosxdx
=∫(1-sinx^2)dsinx
=sinx-(sinx)^3/3 (-π/2,π/2)
=(1-1/3)-(-1+1/3)
=4/3