∫[0,1]dx∫[x,√x]siny/ydy 的二重积分
问题描述：
∫[0,1]dx∫[x,√x]siny/ydy 的二重积分
答
交换积分次序：∫[0,1]dx∫[x,√x]siny/ydy=∫[0,1]dy∫[y²--->y] siny/y dx=∫[0,1] (siny/y)(y-y²)dy=∫[0,1] (siny-ysiny)dy=∫[0,1] sinydy-∫[0,1] ysinydy=-cosy+∫[0,1] yd(cosy)=-cosy+ycosy-∫[0...