Flux across a plane with varying electric field

[oreosama]

Homework Statement

I got home from a test, had an extra credit problem semi memorized and am wondering how I was suppose to solve.

http://i.imgur.com/cIOdSvk.png

A plane with sides $L$ is at $x=3$ . An electric field $E = α y^2 x i + α z^2 y j$ passes through (where $\alpha$ is a constant). Find the flux through the plane. (Givens are $L, \alpha$

Homework Equations

$\Phi = \oint E \cdot dA$

The Attempt at a Solution

Frankly I didn't feel like I knew what I was doing. The plane varies along y and z and the vector for dA will always go in the i direction

$dA i = dydz i$
$E \cdot dA = \alpha y^2 x dydz$
$\int_0^L \int_0^L y^2 x dydz$
$L \alpha x \frac{y^3}{3}|^L_0$
$\frac{L^4}{3} \alpha x$

x=3

$L^4 \alpha$

 

[TSny]

Your work looks correct to me.