积分上限√2,下限0.x^2√（2-x^2）dx 求积分

题目

积分上限√2,下限0.x^2√（2-x^2）dx 求积分

答案

I=∫(0->√2)x^2√（2-x^2）dxletx = 2sinydx = 2cosy dyx=0,y = 0x=√2,y = π/4I=∫(0->π/4)4(siny)^2 (√2)cosy (2cosy)dy=8√2∫(0->π/4) (sinycosy)^2 dy=2√2∫(0->π/4) (sin2y)^2 dy=√2∫(0->π/4) (1-co...