diff --git a/docs/1b/math119.md b/docs/1b/math119.md index 08b2dda..dbbdbdb 100644 --- a/docs/1b/math119.md +++ b/docs/1b/math119.md @@ -422,3 +422,13 @@ Functions can also be replaced to be bounded by the other if necessary. &=\frac 1 4 x^4(2)\biggr|^2_0 \\ &= 8 \end{align*} + +### Double polar integrals + +The differential elements can be directly replaced: + +$$dA=dxdy=\rho d\rho d\phi$$ + +In general, the radius should be the inner integral, and functions converted from Cartesian to polar forms. + +$$\int^{\phi_2}_{\phi_1}\int^{\rho_2}_{\rho_1}f(\rho\cos\phi,\rho\sin\phi)\rho d\rho d\phi$$