Let $M$ be the closed surface that consists of the hemisphere $$M_1: x^2 + y^2 + z^2 = 1,\quad z \ge 0,$$ and its base $$M_2: x^2 + y^2 \le 1,\quad z = 0\, .$$
Let $\mathbf{E}$ be the electric field defined by $\mathbf{E} = (5 x, 5 y, 5 z)$. Find the electric flux across $M$. Write the integral over the hemisphere using spherical coordinates, and use the outward pointing normal. $$\iint_{M_1} \mathbf{E} \cdot d\mathbf{S} = \int_a^b\int_c^d f(\theta, \phi)\,d\theta\,d\phi,$$ where

$a =$ , $b =$ , $c =$ , $d =$ ,

Using $\verb+t+$ for $\theta$ and $\verb+p+$ for $\phi$,
$f(\theta, \phi) =$

$\iint_{M_1} \mathbf{E} \cdot d\mathbf{S} =$

$\iint_{M_2} \mathbf{E} \cdot d\mathbf{S} =$ , so

$\iint_{M} \mathbf{E} \cdot d\mathbf{S} =$ .