Surface Area of of an area - parametric surface

[Dick]

I got a + sign in there. (-1)^2=(+1). You can still simplify some more.

 

[Damascus Road]

Woops, your right:

A(S) = $$\int \int \sqrt{\frac{1}{(1-r^{2})}$$ dA

 

[Dick]

Ok, now you want to integrate over the values of x and y that will cover the spherical cap. That's a circular region, right? That's a good reason to switch to polar coordinates. What is dA in polar coordinates?

 

[Damascus Road]

r^2 sin (phi) dr dtheta dphi

 

[Dick]

A is a region in the x-y plane. Use polar coordinates. Not spherical.