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

## Answer this Question

## Related Questions

- calculus - find the average value of the function f(x,y)=e^(-x^2) over the plane...
- calculus - find the average value of the function f(x,y)=xe^y over the plane ...
- Theorem Calculus - A thin triangle has vertices (0,0), (1,0), and (0,2). Let the...
- Calculus Help!! - Region R is bounded by the functions f(x) = 2(x-4) + pi, g(x...
- Calculus - I'm supposed to find the average value of the function over the given...
- Calculus - Find the volume of the solid generated by revolving the region ...
- Calculus - Find the average value of the function f(x) 8x^2-9x+8 on the interval...
- Calculus - Use the Fundamental Theorem of Calculus to find the area of the ...
- Calc Jacobian - Thanks "I know that the xy region is the line x=y y=0 and y=1- x...
- calculus - a right triangle is formed in the first quadrant by the x- and y- ...