# Double intergral using polar

• May 18th 2011, 12:57 AM
salohcinseah
Double intergral using polar
i'm sorry if this look messy and uni computers does not have latex installed, kindly please help to convert it to latex if possible and thank you in advance

Evaluate the following interral using geometrical interpretation
I= intergral( intergral( (a^2 -x^2 -y^2)^1/2 dxdy , where R is the disk given by
R = {(x,y):x^2+y^2 (smaller or equal than) a^2

the next step that i have done is to change it to intergral( intergral( (a^2 -r^2)^1/2 r.dr.d(digt)

after that i'm lost can any kind soul enlighten me on further steps?

and thank in advance to the guy if he manage to change this question to lastex format.
• May 18th 2011, 01:02 AM
Ackbeet
So as I see it, you've got yourself the integral

$\iint\sqrt{a^{2}-r^{2}}\,r\,dr\,d\theta.$

Is that correct? If so, I would definitely try to figure out the limits for the integrals next. What are those?
• May 18th 2011, 01:15 AM
salohcinseah
the domain given is R = {(x,y):x^2+y^2 (smaller or equal than) a^2
• May 18th 2011, 01:17 AM
Ackbeet
Yes, but since you've got the integral defined in terms of polar coordinates (definitely the way to go here), you'd like to be able to describe your domain in polar coordinates. If you could do that, then you should be able to read off the limits for your integral. So how would you describe your domain in polar coordinates?
• May 18th 2011, 01:26 AM
salohcinseah
i have no idea on how describe the domain in polar coordinates or how to do it, could u mind showing me how?
• May 18th 2011, 01:28 AM
Ackbeet
Well, first describe the region in words. What does this look like? What's its shape?
• May 18th 2011, 01:30 AM
salohcinseah
hemisphere
• May 18th 2011, 01:36 AM
Ackbeet
Quote:

Originally Posted by salohcinseah
hemisphere

No, I don't think you've quite got it. The word "hemisphere" implies three dimensions, but you're only working in two dimensions. What does the region

$\{(x,y):x^{2}+y^{2}\le 1\}$ look like? How about

$\{(x,y):x^{2}+y^{2}\le 4\}?$ And what about

$\{(x,y):x^{2}+y^{2}\le 9\}?$
• May 18th 2011, 01:42 AM
salohcinseah
x^2+y^2 = a circle