- #1

- 52

- 0

## Homework Statement

Use polar coordinates to set up and evaluate the double integral f(x,y) = e

^{-(x2+y2)/2}R: x

^{2}+y

^{2}≤25, x≥0

## The Attempt at a Solution

First I just want to make sure I'm understanding this

my double integral would be

∫[itex]^{\pi/2}_{-\pi/2}[/itex] because x≥0 ∫[itex]^{5}_{0}[/itex] because my radius is 5 (e

^{-(x2+y2)/2}) r dr dθ

and then my inside would become ∫[itex]^{\pi/2}_{-\pi/2}[/itex] ∫[itex]^{5}_{0}[/itex] (e

^{-r2/2}) r dr dθ

can anyone confirm for me that this is correct and give me a brief break down on integrating.

obviously I would use substitution because I have r e

^{r2}but the -1/2 is throwing me a bit when it comes to the substitution.

Also how would i go about changing the limits while I'm substituting.

u= r

^{2}

du = 2r dr

isn't there something I have to do with my limits of integration that involves my u and du?