# Homework Help: Where to start?

1. Nov 28, 2007

### pern_comoto

Okay I have no idea where to start on this example problem:

Use polar coordinates to evaulate the double integral e^((x^2)+(y^2))dydx
[frist (inner) integal lower limit y= -sqrt(4-x^2) upper limit y=0)]
[second (outer) lower limit x=0 upper limit x=2]

When I start doing the integral of e^((x^2)+(y^2))dy I get some really crazy answer and then I dont know if I should put it in polar coordinates before I try and take the integral or after. Can you tell me where to start?

2. Nov 28, 2007

### HallsofIvy

How in the world would you get "some really crazy answer"? It's pretty well known that there is no elementary anti-derivative for $e^{-x^2}$- not even a "crazy" one!

Also, since the problem is to evaluate the integral, I would see no point in changing to polar coordinates after integrating!

What do you start? By doing what the problem says: "use polar coordinates"!
Of course $e^{-(x^2+ y^2)}$ converts to $e^{-r^2}$. Do you know how dydx converts?

To get the limits of integration, draw a picture. $y= -\sqrt{4- x^2}$ is the lower half of the circle $x^2+ y^2= 4$ which has center at the origin and radius 2. x going from 0 to 2 means you are to the right of the y-axis. The region you are integrating over is the lower right quarter of a circle of radius 2. How do r and $\theta$ change to cover that region?