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.