Posted by soffy on Tuesday, June 12, 2012 at 9:01am.
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
=1/2-e^(-1)/2
The area of R is 1/2, so
Average value
= I/(1/2)
=(e-1)/e
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