Polar Coordinates – Finding integration limits in polar coordinates – Exercise 4002

Exercise

Given the double integral

$\int\int_D f(x,y) dxdy$

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

$\{(x,y)|\frac{x^2}{a}\leq y\leq a,-a\leq x\leq a, a>0\}$

Final Answer

$\int_{\frac{3\pi}{4}}^{\pi}d\theta\int_0^{\frac{a\sin\theta}{\cos^2\theta}} f(r\cos\theta,r\sin\theta)\cdot r dr+$

$+\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}}d\theta\int_0^{\frac{a}{\sin\theta}} f(r\cos\theta,r\sin\theta)\cdot r dr+$

$+\int_0^{\frac{\pi}{4}}d\theta\int_0^{\frac{a\sin\theta}{\cos^2\theta}} f(r\cos\theta,r\sin\theta)\cdot r dr$

Solution

Coming soon…

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