Question

Average Value of a function: f(x,y)=xy over the plane region defined by y=x^2 over the interval [0,1]. Please Help!

Answer 1

Claire, I am not exactly sure what you mean. But here is my guess:
f(x.y) = xy = x(x^2) = x^3.
The average value of a function is just \[\int\limits_{-\infty}^{\infty} xP(x)\]
which is \[\int\limits_{0}^{1} x^4 dx\]
and that evaluates to \[x^5 / 5 \therefore 1/5 - 0 \therefore 1/5\]
so 0.2 would be the average