Posted by **Anonymous** on Thursday, April 5, 2012 at 10:01am.

find the average value of the function

f(x,y)=xe^y

over the plane region R is the triangle with vertices (0,0), (1,0) and (1,1)

- calculus -
**Steve**, Thursday, April 5, 2012 at 2:29pm
average value is volume/base area

one boundary of the region is the line y=x

v = ∫[0,1]∫[0,x] xe^y dy dx

= ∫[0,1] (xe^y)[0,x] dx

= ∫[0,1] x(e^x-1) dx

= (e^x(x-1)-x^2/2)[0,1]

= 1/2

area of base = 1/2

avg value = 1

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