# Surface integral

1. Mar 17, 2010

### squenshl

Let S be a parametrised surface given by (x, y, z) = R(u, v) := (u2, v2, u + v), for 0 $$\leq$$ u $$\leq$$ 1 and
0 $$\leq$$ v $$\leq$$ 1. How do I find the integral K := $$\int\int_S$$ z/2 dA.

2. Mar 17, 2010

### quasar987

By definition, this integral is

$$\int_0^1\int_0^1 \frac{u+v}{2}\sqrt{E(u,v)G(u,v)-(F(u,v))^2}dudv$$

where
$$E=R_u\cdot R_u$$
$$F=R_u\cdot R_v$$
$$G=R_v\cdot R_v$$

And this you know how to do.

3. Mar 17, 2010

### squenshl

That's easy. Cheers.