AP® Calculus AB-BC

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Moderate

Finding $k$ From a Table

APCALC-ZMDXKR

Assuming that $ f(x)$ is a continuous function over the interval $[2,10]$, the following table gives the function values for selected values of $x$. Forming a Left Riemann Sum using the intervals of width $2$ suggested by the table, find the value of $k$ given the approximation of the following integral:

$$\int _{ 2 }^{ 10 }{ f( x ) dx } =90$$

$x$ 2 4 6 8 10
f(x) 15 13 10 k 8
A

$-1$

B

$7$

C

$14$

D

$44$