Posted by soffy on .
find the average value of the function f(x,y)=e^(x^2) over the plane region R which is the triangle with vertices (0,0), (1,0) and (1,1)

calculus 
MathMate,
Please check the function for typo, since
f(x,y)=e^(x²) is independent of y.
Assuming no typo,
the region R is bounded between x=0 and x=1, and y=0 and y=x.
So the integegration
dy from 0 to x
dx from 0 to 1.
I=∫∫ye^(x²)dy dx
=∫xe^x² dx
=1/2e^(1)/2
The area of R is 1/2, so
Average value
= I/(1/2)
=(e1)/e