# Evaluating a double integral

1. Jul 13, 2008

### math_04

1. The problem statement, all variables and given/known data

Given the integral shown (in attachment), make a sketch of the region of integration, express the integral with the order of integration reversed and evaluate the integral after reversing the order of integration

2. Relevant equations

3. The attempt at a solution

So i got the limits as y<= x <= 1 and 0 <= y <= 1

But for the function y^2 sin xy dxdy, how should i integrate that. Integration by parts would not work because v= 0 so the whole integral becomes 0. Should i just read it off the table of integrals. if i do that, the integral becomes -y^2cosxy dx rite?

Thanks

#### Attached Files:

• ###### untitled-3.JPG
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2. Jul 13, 2008

### math_04

oh no, attachment pending approval. not again haha.

3. Jul 14, 2008

### Defennder

As said before, if you want quick replies, just host it on imageshack.us or some other image-hosting web service.

4. Jul 14, 2008

### vip_snoopy

hahahaha~~~~~~~~

but why do they need to be approved?

5. Jul 14, 2008

### HallsofIvy

Staff Emeritus
You seem to have done the same thing you did with the previous problem: your "inner" integral goes from x to 1 while the shaded area in your picture is below the line y= x.

6. Jul 14, 2008

### math_04

ohhh my god ur rite hallsofIvy thanks.

Alright, so the limits change but how do u evaluate that integral. Cant do it by parts cause of the reasons i mentioned.