Select the mathematical expression that represents electric flux through a surface in full calculus form.

A uniform electric field of magnitude $E$ makes a constant angle $\theta$ with the normal to a flat surface of area $A$. Select the expression that results from simplifying the general calculus definition of electric flux.

A rectangular panel lies in the $xy$-plane, extending from $x=0$ to $x=L$ and from $y=0$ to $y=W$. The field is $\vec{E}=\left(\frac{E_{0}x}{L}\right)\hat{z}$. Select the correct flux integral setup for the upward normal.

A rectangle has length $L=3.0$ m and width $W=2.0$ m, lying in the $xy$-plane with an upward normal vector. The electric field is $\vec{E}=\left(\frac{12x}{L}\right)\hat{z}$ N/C. Determine the electric flux through the rectangle.

Two students compute the flux through the same flat panel in the $xy$-plane. Student A chooses normal $+\hat{z}$; Student B chooses normal $-\hat{z}$. The field is $\vec{E}=E\left(x\right)\hat{z}$. Select the correct statement regarding their computed flux values.