Question

[CALCULUS III—DOUBLE INTEGRALS] Evaluate by converting to polar coordinates. (figure inside)

Answer 1

\[\int_0^3\int_0^{\sqrt{9-x^2}}(x^2+y^2)^{3/2}\ dydx\]

Answer 2

notes — http://tutorial.math.lamar.edu/Classes/CalcIII/DIPolarCoords.aspx

Answer 3

Let's start by drawing the region.\[\large 0 \le y \le \sqrt{9-x^2}\]Here are the boundaries on y, it appears to be the upper half of a circle, with radius 3.