00:01
So in this question, we are asked to find the average value of the function f of xy equals x times y over the rectangle in the xy plane having vertices at 0 ,0, 02, 42, and 40.
00:17
So what are we going to do? well, we have a formula for the average value of a function over a region in the plane.
00:28
And that formula is we take one over the area of our region times the double integral over the region r of our function of our function f of x, y, da.
00:48
Now in this case, my region r is a rectangle 4 by 2.
00:54
And so the area of this region is 8.
00:58
I'm getting a 1 eighth in front times the double inch.
01:04
Integral of my function f of x y, that's just x times y this time.
01:13
Now i can set this up in either the d y d x or d x, d y direction.
01:21
Since this is a rectangle, i don't think it matters.
01:25
I'll set this up d -y -d -x...