∫(0,1) [x^3 * (1-x^2)^0.5 ]dx
问题描述：
∫(0,1) [x^3 * (1-x^2)^0.5 ]dx
答
设x=sint,dx=costdt,当x=0时,t=0,x=1,t=π/2,原式=∫[0,π/2](sint)^3(cost)^2dt=-∫[0,π/2](sint)^2(cos)^2]d(cost)=∫[0,π/2][1-(cost)^2](cost)^2d(cost)=-∫[0,π/2](cos)^2d(cost)+∫[0,π/2(cost)^4d(cost)=...