Thursday

November 27, 2014

November 27, 2014

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

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 10:10amThe 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

**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 - 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 - The region R is bounded by the x-axis, y-axis, x = 3 and y = 1/(sqrt(...

calculus - a right triangle is formed in the first quadrant by the x- and y- ...