# Double integral question

## Homework Statement

Sketch the region of integration and then evaluate the double integral:

## Homework Equations

$$\int\int$$x2exydA over the region R= {(x,y), y<=x<=1, 0<=y<=1}

## The Attempt at a Solution

I have managed to do half of the problem and integrate it respect to x but then have no idea how to finish the problem.

I mangaged to get upto $$\int$$ey(2/y2-2/y3-1/y)+ey2(y-2/y+2/y3) dy

can someone please tell me how to finish it or if i have done something wrong so far??

cheers

Last edited:

tiny-tim
Homework Helper
Welcome to PF!

Hi kieranl! Welcome to PF! (have a ≤ )
$$\int\int$$x2exydA over the region R= {(x,y), y<=x<=1, 0<=y<=1}

I mangaged to get upto $$\int$$ey(2/y2-2/y3-1/y)+ey2(y-2/y+2/y3) dy

uhh? start again, and integrate over dy first! but if i integrated by dy first wouldnt i end up with an answer containing y's and not numbers??

tiny-tim
Homework Helper
but if i integrated by dy first wouldnt i end up with an answer containing y's and not numbers??

If you integrate with respect to dy, then you eliminate y, and only have x's.

but i have to integrate over y<=x<=1 for dx so the final answer would then contain y's?

Draw a picture of the region R. Then use the picture to write R in the form

R={(x,y):a<x<b, f(x)<y<g(x)}.

tiny-tim
Hi kieranl! (have an integral: ∫ and a ≤ )
whether you do it over x first or over y first is up to you. 