Question

wtf how do you do double integrals in polar co-ordinates?

Answer 1

polar coordinates are in terms of the angle and the radius/distance
depends on what shape you have on how difficult it can be

Answer 2

Same way you do them using other systems, though usually you have an extra factor of r.

\[\large \int_Df = \int_{x_0}^{x_1}\int_{y_0}^{y_1} f(x,y)\ dydx = \int_{\theta_0}^{\theta_1}\int_{r_0}^{r_1}f(r, \theta) \cdot r\ drd\theta \]

Answer 3

thanks for the answers

Answer 4

The "r*dr*dtheta" part of polpak's answer reprents an element of area (working in 2D plane, polar coordinates). It is at radius r, and its distance from origin is r to r+dr, and its width is ... angular width dtheta, but at radius r, so linear width r*dtheta. So you are adding up (integrating) function value f(r,theta) times area of a small patch, for all the patches in the radius domain r1 < r < r2, and the angular direction domain theta1 < theta < theta2. It does not matter in which order you do the integrals (for well behaved functions).