Question

二重积分

有关二重积分的题目，有图

Answer 1

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

Answer 2