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Polar Coordinates – Finding integration limits in polar coordinates – Exercise 3997

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)|1\leq x\leq 2,x\leq y\leq\sqrt{3}x\}

Final Answer

\int_{\frac{\pi}{4}}^{\frac{\pi}{3}}d\theta\int_{\frac{1}{\cos\theta}}^{\frac{2}{\cos\theta}} f(r\cos\theta,r\sin\theta)\cdot r dr

Solution

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