米娅哈利法

米娅哈利法:

∫∫|y-x^2|dxdy=[-1,1]∫dx[0,x^2]∫(x^2-y)dy+[-1,1]∫dx∫[x^2,1](y-x^2)dy

=[-1,1]∫x^4/2dx+[-1,1]∫(1/2-x^2-x^4/2)dx

=x^5/10 | [-1,1] + (x/2-x^3/3-x^5/10 ) | [-1,1]

0.333333333

0.333333333

∫∫(xy+y^2+1)dxdy=[0,2π]∫dθ[0,2]∫(cosθsinθp^2+(sinθ)^2p^2+1)pdp

=[0,2π]∫(4sin2θ-4cos2θ+20)dθ

=(20θ-2sin2θ-2cos2θ) | [0,2π]

=40π"