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Polar Coordinates – Finding integration limits in polar coordinates – Exercise 3986

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^2+y^2\leq ax, a>0

Final Answer

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

או

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

Solution

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