Integrating Double Integrals: From 0 to 1 & -x to 0

[Kreamer]

[tex]\int[/tex][tex]^{1}_{0}[/tex][tex]\int[/tex][tex]^{0}_{-x}[/tex] [tex]\frac{ysin(pi*y^2)}{1+y}[/tex] dydx

Not exactly sue how to start this. I know that I need to integrate with respect to y first then use that solution and integrate again with respect to x however I do not believe integrating the initial problem is possible. Is there another way to go about solving this?

 

[Dick]

Change the order of integration. If you are going to integrate dx first, what are the x limits?

 

[Kreamer]

pretty sure the input got messed up and i couldn't fix it. limits are -x to 0 for y and 0 to 1 for x

 

[Dick]

pretty sure the input got messed up and i couldn't fix it. limits are -x to 0 for y and 0 to 1 for x

The input is readable. I mean change the order of integration. Draw a picture of the domain in the x-y plane. If you change the order of integration you have to figure out new limits.

 

[Kreamer]

I am not following. I can't even begin to integrate it, regardless of the limits.

 

[Dick]

I am not following. I can't even begin to integrate it, regardless of the limits.

The integrand is a function only of y. You could certainly integrate that dx. That's the trick. Change the limits so you integrate dx first. Once you do that integration, you'll wind up with something you CAN integrate dy.

 

[Char. Limit]

[tex]\int^{1}_{0} \int^{0}_{-x}\frac{ysin(\pi y^2)}{1+y} dy dx[/tex]

Not exactly sue how to start this. I know that I need to integrate with respect to y first then use that solution and integrate again with respect to x however I do not believe integrating the initial problem is possible. Is there another way to go about solving this?

A tip with the LaTeX notation, it works better if you put the entire expression inside single LaTeX tags as I did above when I quoted your post. I don't believe that quotes can be quoted, though, so here's the expression again if you want to read it.

[tex]\int^{1}_{0} \int^{0}_{-x}\frac{ysin(\pi y^2)}{1+y} dy dx[/tex*]

 

[Kreamer]

Would the limits still be 0 to 1 for x then -x to 0 for y? I am running on 3 hours of sleep so I feel completely lost sorry.

If so switching the order would only add an x to the equation then plug in a 1 for the x and a subtracting the 0 form of the equation giving me a single integral of just what's above... right?

I know it isn't really what you are supposed to do or may like to do but is there anyway you can show me the steps of solving it? I am better at learning by following. Its a practice problem, not homework or anything. Not taking credit for your work for a grade or anything

 

[Dick]

Would the limits still be 0 to 1 for x then -x to 0 for y? I am running on 3 hours of sleep so I feel completely lost sorry.

If so switching the order would only add an x to the equation then plug in a 1 for the x and a subtracting the 0 form of the equation giving me a single integral of just what's above... right?

I know it isn't really what you are supposed to do or may like to do but is there anyway you can show me the steps of solving it? I am better at learning by following. Its a practice problem, not homework or anything. Not taking credit for your work for a grade or anything

Still best if you do it. The domain is the triangle formed by the three points (0,0), (1,0) and (1,-1), right? Did you draw that? Now you want to integrate your function on that dx first. Draw a horizontal line through the triangle at a value of y. What are the x limits in terms of y?

 

[Kreamer]

I am sorry my brain is just fried, got to go take the test now. Wish me luck :/

 

[Dick]

I am sorry my brain is just fried, got to go take the test now. Wish me luck :/

Good luck!

 

[Char. Limit]

I wish you luck.