Double integral Help

[Sylva]

Hey,

I've been stuck on this problem for quite some time:

J = ∫0 ->4 ∫ sqrt(x) -> 2   (1 + y^2 * cos(x * sqrt(y))) dydx

The cos (x * sqrt(y)) is the one causing trouble. I can't seem to find a way to integrate this. I even tried to turn it to polar coordinates but nothing seems to work.

What am I doing wrong? Could someone point me in the right direction?

Another thing I don't understand with multiple integrals : How do you know if it represents a Volume?

Thanks in advance.

PS: Sorry for my english, it's not my native language.

[studiot]

It is usually the limits that trip people up with multiple integrals.

Have you identified which variable you must integrate first with respect to and why?

Hint what cannot appear in the limit of the integral you are undertaking?

What is then the effect on the limits of the second integral?

For the benefit of all please confirm this is the integral you are attempting.

[math]J = \int\limits_0^4 {\int\limits_{\sqrt x }^2 {\left( {1 + {y^2}\cos \left[ {x\sqrt y } \right]} \right)} } dydx[/math]

 

Edited October 12, 2017 by studiot

[Sylva]

Yes, this is the integral I'm attempting.

Are you implying that I should change the limits so the limit of y depends on the value of x?

This implies that I'm gonna have to integrate dx before dy.

I'm not sure how this will help to resolve the problem of integrating cos[x√y] .

[studiot]

9 minutes ago, Sylva said:

Are you implying that I should change the limits so the limit of y depends on the value of x?

How did you arrive at that conclusion?

When you integrate with respect to y, how do you handle any instances of  'x' ?

Edited October 12, 2017 by studiot

[Sylva]

Looks like I finally got the good result by changing the limits.

Was it actually possible to do it without changing the values? I may be missing some notions that would've helped me do it...

 

[studiot]

Glad to see you persisted to your own conclusion, without spoonfeeding.

+1

 

Motivavation is all.