定积分∫√(cosx-cos^3xdx) 上面二分之派,下面负二分之派

问题描述:

定积分∫√(cosx-cos^3xdx) 上面二分之派,下面负二分之派

=∫(-π/2,π/2)√cosx*|sinx| dx (被积函数为偶函数)
=2∫(0,π/2)√cosx*sinx dx
=-2∫(0,π/2)√cosxdcosx
=(-4/3)(cosx)^(3/2)|(0,π/2)
=4/3