Posted by **mabel** on Monday, April 2, 2012 at 3:30am.

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 -
**MathMate**, Monday, April 2, 2012 at 10:10am
The triangle is bounded by

x-axis

x=1, and

y=x.

The integrals can be carried out in order dx, then dy or vice-versa.

However, integrating with respect to dy first makes for an easier integration (in the evaluation of I).

Be very sure you understand how the limits are obtained. Draw a sketch of the triangle, and follow the limits, and it will be easy to visualize how the limits can be found.

Area, A = ∫∫dxdy

Limits of integration

y from 0 to x

x from 0 to 1

Integral of values

I=∫∫xe^ydydx

within the same limits

Average value

= I/A

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