Double integrals + Change of variables

[babbagee]

Ok, i have a problem with this double integral. I am having a hard time finding the limits. The question is

Evaluate
$$\iint \frac{dx\,dy}{\sqrt{1+x+2y}}\$$

D = [0,1] x [0,1], by setting T(u,v) = (u, v/2) and evaluating the integral over D*, where T(D*)=D

Can some one help me find the limits, and explain the process of getting those limits.

Thanks in advance

 

[arildno]

Are you REQUIRED to do that change of variables?
You could integrate it directly..

 

[babbagee]

Yes, because there are some problems which say evaluate the integral with change of variable but then check it by using an iterated integral. So the answer is yes, i have go use change of variable, and even though i don't need to use it was to get practice at it.

Thanks

 

[babbagee]

anybody?

 

[AlexContourPlus]

anybody?

Somebody is always here but not your wishing somebody.
Can you find the integration (to x variable) of 1/root(a+x) ?

 

[HallsofIvy]

I THINK what you are saying is that you want to use the substitution u= x, v= 2y.
Of course, du= dx and dv= 2dy or dy= (1/2)dv.

In terms of u and v, the integral becomes
$$\frac{1}{2}\int \frac{du\,dv}{\sqrt{1+u+v}}$$

The only problem now is finding D*. The boundaries of D are x= 0, x= 1, y= 0, y= 1.
Okay, when x= 0 what is u? When x= 1, what is u? When y= 0, what is v? When y= 1, what is v? That gives you D* and the limits of integration.

 

[AlexContourPlus]

Oh well, sorry for my bad English, I didn't read the whole OP and thought he didn't know how to solve it, but he should say the same as you did anyway, I know that for certain

 

[babbagee]

Thanks

I thought about the problem a little harder and i did the same exact thing you did, so thanks for your help.

 

[Krypton]

What is the non-graphing method to find the new limits ? Someone please,,,,,...!