First slide

Evaluation of definite integrals

Question

The greatest value of the function $F (x) =$
$\int_{4}^{x} (t^{2} - 8 t + 16) d t on [0, 5]$ is

Moderate

A

5
B

$1 / 3$
C

4
D

$2 / 3$

Solution

$F^{'} (x) = x^{2} - 8 x + 16 = (x - 4)^{2} > 0$ for $x \in [0, 5] - {4}$
So the greatest value of $F$ is $F (5)$
$= \int_{4}^{5} (t - 4)^{2} d t = \frac{1}{3}$

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