# Convert double integral to polar

• Oct 22nd 2008, 11:44 PM
bamptom
Convert double integral to polar
Hi Guys / girls

I am going through my home work for uni and i have to calculate the integral of the following by transforming to polar coordinates. This fine except i just cant get my head around how to do this.(Angry)

The problem is -//(3y-x)dydx 0<x<3, -sqrt(9-x^2) < y < sqrt(9-x^2)

• Oct 23rd 2008, 12:37 AM
mr fantastic
Quote:

Originally Posted by bamptom
Hi Guys / girls

I am going through my home work for uni and i have to calculate the integral of the following by transforming to polar coordinates. This fine except i just cant get my head around how to do this.(Angry)

The problem is -//(3y-x)dydx 0<x<3, -sqrt(9-x^2) < y < sqrt(9-x^2)

Have you drawn the region of integration?

Note: $\displaystyle -\sqrt{9-x^2} < y < \sqrt{9-x^2}$ is equivalent to the interior of the circle $\displaystyle x^2 + y^2 = 9$.
$\displaystyle 0 < x < 3$ means you want the right half of this circle ......

Can you define this region using polar coordinates? That will give you the integral terminals.

And you know $\displaystyle dx \, dy \rightarrow r \, dr\, d\theta$, right?
• Oct 23rd 2008, 12:57 AM
bamptom
Are they 0<Theta<pi and 0<r<3 ??

And does (3y-x)dydx >>>>> // (rcostheta + 3rsintheta)rdrdtheta

I really do appreciate your help!
• Oct 23rd 2008, 02:02 AM
bamptom
??
Can anyone tell me if im on the right track here?
• Oct 23rd 2008, 03:33 AM
mr fantastic
Quote:

Originally Posted by bamptom
Are they 0<Theta<pi and 0<r<3 ??

[snip]

No. Have you drawn the region like I suggested? What's the polar coordinates of (0, -3) and (0, 3) .....? Will $\displaystyle 0 < \theta < \pi$ give you those points .....?

Quote:

Originally Posted by bamptom
[snip]
And does (3y-x)dydx >>>>> // (rcostheta + 3rsintheta)rdrdtheta

I really do appreciate your help!

No. How can you substitute $\displaystyle x = r \cos \theta$ and $\displaystyle y = r \sin \theta$ into $\displaystyle 3y - x$ and get $\displaystyle r \cos \theta + 3r \sin \theta$ ....?

By the way, don't bump.