有关二重积分的题目,有图

答：
更改积分顺序,否则做不了.
积分区域如图：
原积分
=∫(1到2)dy∫(y到y^2)sin(πx/(2y))dx
=∫(1到2)(y到y^2) [(2y/π)*[(-cos(πy^2/(2y))-(-cos(πy/(2y)))]]dy
=∫(1到2)(y到y^2) [(2y/π)*[(-cos(πy/2)+cos(π/2))]]dy
=∫(1到2)(y到y^2) -(2y/π)(cos(πy/2))dy
=-(4y/π^2)(sin(πy/2))-(8/π^3)(cos(πy/2))|[1到2]
=-(8/π^2)(sinπ)-(8/π^3)(cosπ)+(4/π^2)(sin(π/2))+(8/π^3)(cos(π/2))
=8/π^3+4/π^2