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AP® Calculus AB-BC

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Solve For K Average Value

APCALC-LSNXAB

Using a Midpoint Riemann approximation on the interval $[0, 6]$ with $3$ equal subintervals, find $k$ if the average value of $f( x ) =2{ x }^{ 2 }+k$ is equal to $20$.

A

$\cfrac{50}{3}$

B

$\cfrac{20}{3}$

C

$-\cfrac{10}{3}$

D

$-\cfrac{52}{3}$