画图看二次积分的区域
D={(x,y)|0≤x≤1,x≤y≤1}
={(x,y)|0≤y≤1,0≤x≤y}
于是
∫(上限1,下限0)dx∫(上限1,下限x)siny^2dy
=∫∫(D)siny^2dxdy
=∫(上限1,下限0)dy∫(上限y,下限0)siny^2dx
=∫(上限1,下限0)ysiny^2dy
=(1/2)∫(上限1,下限0)siny^2dy^2
=(-1/2)cosy^2|(0→1)
=(1-cos1)/2