From ecef4402e5f86e1445f0420a35c8520168506c60 Mon Sep 17 00:00:00 2001
From: eggy <danielchen04@hotmail.ca>
Date: Tue, 7 Feb 2023 11:19:15 -0500
Subject: [PATCH] math119: polar integral intro

---
 docs/1b/math119.md | 10 ++++++++++
 1 file changed, 10 insertions(+)

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.
+
+$$\int^{\phi_2}_{\phi_1}\int^{\rho_2}_{\rho_1}f(\rho\cos\phi,\rho\sin\phi)\rho d\rho d\phi$$