极坐标下的二重积分

Polar coordinates rewrite both region and area

A worked volume between paraboloids

The Gaussian integral

When to reach for polar

Converting $\iint_D f\, dA$ to polar coordinates produces which differential?

$\iint_D (x^2 + y^2)\, dA$ over the disk of radius $2$ becomes which polar integral?

The polar computation over the first quadrant gives $\iint e^{-x^2 - y^2}\, dA = \pi/4$. What follows for $\int_0^\infty e^{-x^2}\, dx$?

Give $\iint r\, dr\, d\theta$ over the sector $0 \le r \le 3$, $0 \le \theta \le \pi/2$, in the form a*pi/b like 5*pi/2.

The solid between $z = x^2 + y^2$ and $z = 2 - x^2 - y^2$ has volume computed as $2\pi \int_0^1 (2r - 2r^3)\, dr$. Give the volume, in the form d*pi like 3*pi.