1. ## Double Integration problem

Hi There,
I hope its ok to post here as i didn't see a group for Integration....

I have this problem in my studyguide which provides a solution but no working. I cannot figure out the steps to get it. Any help will be very much appreciated.
Here goes

Sketch the region R and calculate the doubleIntegral for

f(x,y)=sin(x+y)

R={(x,y) | x >=0, y>=0 and x+y =< π} (this last term is pi)

The answer to this is π ie pi ie 180 degrees.

I know that with the double integral the first integral must have the constants, but seeing as we have a non-constant for x and y I don't know how to tackle it

Many thanks

PS I tried using the math tag but it removed and changed some of the characters

2. make a sketch, you'll be able to do it from there.

3. hm...

try like this ...

sorry my bad.... didn't think it please someone delete this post ....

4. Thanks, to be honest I don't undestand the solution but possibly can you just explain how you got to your values for the integrals ie:

for the double integral I thought I could integrate from

pi-x to 0 for the first one
and
pi - y to 0 for the 2nd

How come were you able to use pi and not pi-x as per the boundary line x+y<=pi ?

5. Originally Posted by iva
Thanks, to be honest I don't undestand the solution but possibly can you just explain how you got to your values for the integrals ie:

for the double integral I thought I could integrate from

pi-x to 0 for the first one
and
pi - y to 0 for the 2nd

How come were you able to use pi and not pi-x as per the boundary line x+y<=pi ?
sorry for that one up there ...I'm little sleepy

your line x+y = pi crosses x axis at point "pi" and so and y axis at the point "pi" now only for which type of integration are you preferring you'll do

$\displaystyle \int _0 ^{\pi} dx \int _0 ^{\pi - x } \sin {(x+y) } dy$

or

$\displaystyle \int _0 ^{\pi} dy \int _0 ^{\pi - y } \sin {(x+y) } dx$

6. Ah thanks I get it now , I was the sleepy one. All made sense after you pointed out the intersection of the line with the axis and if i had sketched it properly ( only made a rough drawing ) I would have seen that . Thanks guys!