设是由矩形区域|x|

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设是由矩形区域|x|

设是由矩形区域|x|
设是由矩形区域|x|

设是由矩形区域|x|
I=∫[0,2]∫[-1,1]|y-x^2|dxdy
=∫[-1,1]∫[0,x^2]|y-x^2|dydx+∫[-1,1]∫[x^2,2]|y-x^2|dydx
=∫[-1,1]∫[0,x^2](x^2-y)dydx+∫[-1,1]∫[x^2,2](y-x^2)dydx
=∫[-1,1](x^2*y-1/2*y^2)|[0,x^2]dx+∫[-1,1](1/2*y^2-x^2*y)|[x^2,2]dx
=∫[-1,1]1/2*x^4dx+∫[-1,1](2-2x^2+1/2*x^4)dx
=∫[-1,1](x^4-2x^2+2)dx
=1/5*x^5-2/3*x^3+2x|[-1,1]
=2*(1/5-2/3+2)
=46/15.