求二重积分,具体见图。
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(4)∫∫(D) (x+2y)dxdy
=∫(0,2)dy∫(y,2y) (x+2y)dx
=∫(0,2)dy*(x^2/2+2xy)|(y,2y)
=∫(0,2) 7y^2/2 dy
=(7/6)*y^3|(0,2)
=28/3
(5)∫∫(D) xy^2 dxdy
=∫(0,1)dx∫(x,√x) xy^2dy
=∫(0,1)dx*(xy^3/3)|(x,√x)
=(1/3)*∫(0,1) [x^(5/2)-x^4]dx
=(1/3)*[(2/7)x^(7/2)-(1/5)x^5]|(0,1)
=1/35
=∫(0,2)dy∫(y,2y) (x+2y)dx
=∫(0,2)dy*(x^2/2+2xy)|(y,2y)
=∫(0,2) 7y^2/2 dy
=(7/6)*y^3|(0,2)
=28/3
(5)∫∫(D) xy^2 dxdy
=∫(0,1)dx∫(x,√x) xy^2dy
=∫(0,1)dx*(xy^3/3)|(x,√x)
=(1/3)*∫(0,1) [x^(5/2)-x^4]dx
=(1/3)*[(2/7)x^(7/2)-(1/5)x^5]|(0,1)
=1/35
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