∫x^2arcsinx/(√1-x^2)dx上限为1下限为0
问题描述：
∫x^2arcsinx/(√1-x^2)dx上限为1下限为0
计算这个反常积分
答
∫(0->1) x^2arcsinx/(√1-x^2) dxletx = sinydx = cosy dyx=0, y=0x=1 , y =π/2∫(0->1) x^2arcsinx/(√1-x^2) dx=∫(0->π/2) y(siny)^2 dy=(1/2)∫(0->π/2) y( 1-cos2y) dy= (1/2) [y^2/2](0->π/2) -(1/2) ∫(...