# Flux of vector field

1. Apr 21, 2009

### -EquinoX-

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

Compute the flux of the vector field, \vec{F} , through the surface, S.
$$\vec{F} = 7\vec{r}$$ and S is the part of the surface $$z = x^2 + y^2$$ above the disk $$x^2 + y^2 \leq 4$$ oriented downward.

2. Relevant equations

3. The attempt at a solution

$$\int\limits_R (7x\vec{i} + 7y\vec{j} + (x^2 + y^2)\vec{k}) \cdot (2x\vec{i} + 2y\vec{j} - k) dA$$
$$\int\limits_R (14x^2 + 14y^2 - (x^2 + y^2)) dA$$
$$\int\limits_R (13x^2 + 13y^2) dA$$
$$13 \int\limits_R (x^2 + y^2) dA$$
$$13 \int^{2\pi}_0\int^4_0 r^3 dA$$
$$13 \int^{2\pi}_0 64 dA$$

is this correct?