I have the following question:

Express as an area integral in polar co-ordinates the area of the surface z = 5 + xy lying over the annulus defined by 2<x^2 + y^2<3. Hence evaluate the area in terms of pi.

I know i have to get the function:

g(r,0) = sqrt 1 + (df/dr)^2 + (df/d0)^2

then evaluate it over the interval 2 to 3.

The problem is i cant seem to get the required answer 13.628pi. All my answers are nuts!!!

are the partial derivatives 0^2 and r^2 ?

and does the 5 in the function get added to the 1 in g(x,y)?

In other words should I have

g(r, 0) = sqrt 6 + 0^2 + r^2 ??

N.B. 0 is meant to be theta.