Average value of function

1. Feb 2, 2009

Master J

To find the average value of a function of one variable, you integrate it and multiply it by 1/(b - a) , where b and a are the limits of integration , uper and lower, respectively.

But how does one do this for a function of two variables, defined on a rectangle?

2. Feb 2, 2009

Dick

The same way, basically. Integrate the function over the rectangle and divide by the area of the rectangle.

3. Feb 3, 2009

Master J

Thanks.

Well I am trying a question. The integrand is (x^2)y. The domain is [2,4] * [-6,6].

Now when I integrate it with respect to y first, it goes to zero. It does not go to zero when you start with x. How is this possible?

4. Feb 3, 2009

gabbagabbahey

Bad math. ....It should be zero in both cases, try showing us what you are doing when you integrate it over x first....

5. Feb 3, 2009

Master J

Possibly!

Ah I see what I've been doing wrong! I don't even need to work out the average value, since it integrates to zero, as it should, since it is evenly distributed in the positve and negative y areas!

Last edited: Feb 3, 2009