# Calculate ∫∫x^2 dS

1. Jan 3, 2012

### bugatti79

1. The problem statement, all variables and given/known data

Calculate ∫∫x^2 dS where S is the triangle with corners (1,1,0) (0,1,0) and (0,0,1)

The triangle is the graph of g(x,y)=1-x-y

One integral can be $\displaystyle \sqrt3 [\int_{0}^{1}(\int_{0}^{1-x}x^2dy)dx]$

I calculate the other one to be

$\displaystyle \sqrt3 [\int_{0}^{1}(\int_{0}^{1-y}(1-y)^2dx)dy]$

but I dont get the same answer...can some one point it out?

Thanks

2. Jan 3, 2012

### Staff: Mentor

Re: Integrals

The integrand, x2, should not change when you change the order of integration.

3. Jan 3, 2012

### bugatti79

Re: Integrals

OK, thanks. I am wondering did I come across situations where one does change the integrand or perhaps I am confusing it with changing the limits when there is a u substitution involved etc?

thanks

4. Jan 3, 2012

### SammyS

Staff Emeritus
Re: Integrals

I'm pretty sure the triangle is in the plane, y+z = 1 .