# surface integral problem

• Jul 6th 2013, 08:52 AM
DonnieDarko
surface integral problem
So, how to solve this integral. I tried to solve it, but solution doesn't fit solution that my classmates got, nobody go the same result, any help?

$\displaystyle y= \sqrt{2} -x$
$\displaystyle x^{2} + y^{2} =\sqrt{2}$
$\displaystyle x\geq 0$
$\displaystyle y=x^{2}$

btw, these are the functions we have. and i know how to sketch it, but the borders of integral may be a problem
• Jul 6th 2013, 09:18 AM
HallsofIvy
Re: surface integral problem
There is no integral here. What is the integrand and what surface are you integrating over?
• Jul 6th 2013, 10:57 AM
DonnieDarko
Re: surface integral problem
Oh, I'm sorry, i wasn't clear enough. So, I need to integrate surface bounded with these curves.
So, when I sketch it, I have 1/4 of a circle, which is easy to integrate, then i need to find integral of a surface bounded with intersection of parabola and and y= 2^1/2 - x.
So I was thinking to solve it by splitting it in two parts, then integrating one plus the other.
• Jul 6th 2013, 12:39 PM
HallsofIvy
Re: surface integral problem
I still have no clue what you mean. I have never heard of "integrating a surface". I have heard of integrating a given function over a surface or finding the area of a surface (equivalent to integrating 1 over the surface). Also, I am used to a "surface integral" as referring to a surface in three dimensions but your equations have only two variables, x and y. Is this in the xy-plane? Finally, I am confused by the fact that these curves divide the first quadrant into four separate regions. Which do you want to integrate over?
• Jul 6th 2013, 02:41 PM
DonnieDarko
Re: surface integral problem
Here, I attached a pic from a book i'm working from, too bad its not in eng, but you can see that formula with two integrals, thats the way we are finding surface of a 2-dim body. So, basic thing is we make two integrals dxdy and the first have constant boundaries and second have boundaries as functions in respect of x. And thats, in short, how we found surface of a 2-dim figure.
Got it?