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討論串[微積] 二重積分
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Ω={(x,y)│x^2+y^2≦1}. A=∫∫ sin(x^2)cos(y^2)dxdy. Ω. B=∫∫ cos(x^2)sin(y^2)dxdy. Ω. Let C=A+B. Then C is equal to an iterated integral. which is express
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內容預覽:
u=x+y. v=y. then. x=u-v. y=v. dx/du=1, dx/dv=-1. dy/du=0, dy/dv=1. |J|=1. then. x-y^2=(u-v)-v^2>0. (v+1/2)^2<u+1/4. -√(u+1/4) -1/2 < v < √(u+1/4) -1/2
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