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Polar Coordinates – Finding integration limits in polar coordinates – Exercise 3994

Exercise

Given the double integral

\int\int_D f(x,y) dxdy

Calculate the integration limits in polar coordinates where D is the domain

\{(x,y)|0\leq x\leq 1,0\leq y\leq1-x\}

Final Answer

\int_0^{\frac{\pi}{2}}d\theta\int_0^{\frac{1}{\sin\theta+\cos\theta}} f(r\cos\theta,r\sin\theta)\cdot r dr

Solution

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