# Minimizing a double integral

• March 29th 2009, 07:56 PM
antman
Minimizing a double integral
What region r in the xy plane minimizes the value of $\int\int_{R}$ $(x^{2}+y^{2}-9)dA$ ? What are the reasons?
• March 29th 2009, 09:01 PM
robeuler
Quote:

Originally Posted by antman
What region r in the xy plane minimizes the value of $\int\int_{R}$ $(x^{2}+y^{2}-9)dA$ ? What are the reasons?

What kind of graph do you think of when you see x^2+y^2-9?

You should be reminded of a circle, of radius 3. You should also think about converting to polar coordinates.
• April 5th 2009, 03:56 PM
antman
I recognize the equation of a circle but am unsure of how to answer it. Would R be the set of points (x,y) such that x^{2}+y^{2} is greater than 9?