How do I evaluate a double integral with a trigonometric function?

[math_04]

Homework Statement

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

Homework Equations

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

 

[math_04]

oh no, attachment pending approval. not again haha.

 

[Defennder]

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

 

[vip_snoopy]

hahahaha~~~~~~~~

but why do they need to be approved?

 

[HallsofIvy]

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.

 

[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.