被积函数是偶函数所以原式=2∫(0-->1)4x^2dx/[1+√(1-x^2)] 做变换x=sint
则上式等于2∫(0-->π/2)4(sint)^2costdt/1+cost=8∫(0-->π/2)(1-cos^2t)costdt/(1+cost)
=8∫(0-->π/2)(1-cost)costdt 下面自己算吧
被积函数是偶函数所以原式=2∫(0-->1)4x^2dx/[1+√(1-x^2)] 做变换x=sint
则上式等于2∫(0-->π/2)4(sint)^2costdt/1+cost=8∫(0-->π/2)(1-cos^2t)costdt/(1+cost)
=8∫(0-->π/2)(1-cost)costdt 下面自己算吧