# calculus

posted by .

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 -

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

## Similar Questions

1. ### Calculus

Find the volume of the solid generated by revolving the region enclosed in the triangle with vertices (4.6,4.6), (4.6,0), (6.7,4.6) about the x-axis.
2. ### Calculus

Use the Fundamental Theorem of Calculus to find the area of the region bounded by the x-axis and the graph of y = 4 x3 − 4 x. Answer: (1) Use the Fundamental Theorem of Calculus to find the average value of f(x) = e0.9 x between …
3. ### calculus

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)
4. ### Calculus

I'm supposed to find the average value of the function over the given interval. f(x) = sin(nx), interval from 0 to pi/n, where n is a positive integer. I know the average value formula, and I know that the integral of that function …
5. ### calculus

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)
6. ### Calculus Help!!

Region R is bounded by the functions f(x) = 2(x-4) + pi, g(x) = cos^-1(x/2 - 3), and the x axis. a. What is the area of the region R?
7. ### Theorem Calculus

A thin triangle has vertices (0,0), (1,0), and (0,2). Let the density function at any given point on the triangle be represented by ρ(x,y)=1+3x+y. The mass of the triangle can be represented by p/q, where p and q are coprime positive …
8. ### Calculus

Find the average value of the function f(x) 8x^2-9x+8 on the interval [3,5]. Find the value of the x-coordinate at which the function assumes it's average value The average value is ?
9. ### Calculus

Find the average value of the function over [1,3] and all values of x in the interval for which the function: f(x)= 4(x^2+1)/x^2 equals its average value.
10. ### Calculus

the region D is the triangle with vertices (1,1) (3,1) (3,2) about the y-axis find r(x) and h(x) using the shell method. My teacher got r(x)=x and h(x)=(1/2x+1/2)-1 but how did he get the equation for h(x)?

More Similar Questions