The Honor Society decided to have t-shirts made for each member. There is a screen printing fee of $15 and each t-shirt costs $4
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Apparently my answer was unclear the first time?
The flux of <em>F</em> across <em>S</em> is given by the surface integral,
Parameterize <em>S</em> by the vector-valued function <em>r</em>(<em>u</em>, <em>v</em>) defined by
with 0 ≤ <em>u</em> ≤ π/2 and 0 ≤ <em>v</em> ≤ π/2. Then the surface element is
d<em>S</em> = <em>n</em> • d<em>S</em>
where <em>n</em> is the normal vector to the surface. Take it to be
The surface element reduces to
so that it points toward the origin at any point on <em>S</em>.
Then the integral with respect to <em>u</em> and <em>v</em> is