# 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

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

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