polar coordinates

[fsubx]

Hey I need some help with a homework problem. I problem asks to convert the double integral from rectangular to polar coordinates and evaluate

 

And since I don't know how to create the symbols I will do my best to write out the problem in English.

 

The bounds of the outer integral are from 0 to a

The bounds of the inner integral are from 0 to the square root of (a^2_x²)

 

The function being integrated is (x dydx)

 

Thanks

[Schrödinger's hat]

And since I don't know how to create the symbols I will do my best to write out the problem in English.

 

You can use

[math]

and

[/math]

tags and LaTeX to produce symbols.

Ie.

[math]\int_{x=0}^a\int_{y=0}^{\sqrt{a^2 - x^2}}x\;dy\,dx[/math]

Will produce:

[math]\int_{x=0}^a\int_{y=0}^{\sqrt{a^2 - x^2}}x\;dy\,dx[/math]

 

Hey I need some help with a homework problem. I problem asks to convert the double integral from rectangular to polar coordinates and evaluate

Did you do anything work so far? Exactly where are you stuck?

It's good form to post your attempt along with the question here. That way we can address the points where you are stuck without just handing you the answer.

 

At any rate, here's a few things which might get you started if you're completely stuck:

 

What does [math]y = \sqrt{a^2 - x^2}[/math] remind you of?

Perhapsit will be more apparent if it's written [math]x^2 + y^2 = a^2[/math]

What would that mean for the limits of r?

 

If you draw a circle, which angles result in a positive x value?

Perhaps you could draw this region in cartesean coordinates,