Optimizing Integration: Converting to Polar Coordinates

[PsychonautQQ]

Homework Statement

Evaluate the integral by changing to polar coordinates.

Double Integral: (x^2+y^2)dydx, where dy is bound between 0 and (4-x^2)^(1/2) and dx is between and -2 and 2

The Attempt at a Solution

okay so I can turn this into
Double Integral: (r^2)rdrdθ

My question is on the parameters of dr and dθ
I really want to say dr goes from 0 to 2.
does dθ go from 0 to 2∏

 

[Simon Bridge]

If that is what you really want to say, then what is stopping you?

note:
it is not dr that goes from 0 to 2, it is r that does that. etc.

 

[Mark44]

Homework Statement

Evaluate the integral by changing to polar coordinates.

Double Integral: (x^2+y^2)dydx, where dy is bound between 0 and (4-x^2)^(1/2) and dx is between and -2 and 2

The Attempt at a Solution

okay so I can turn this into
Double Integral: (r^2)rdrdθ

My question is on the parameters of dr and dθ
I really want to say dr goes from 0 to 2.
does dθ go from 0 to 2∏

Can you describe, in words, the region over integration takes place? If you understand this region, you'll pretty much have answered your question about θ.

 

[LCKurtz]

I second Mark's comment. Tell us what the region looks like. For all we know, your original integral may be set up wrong.