First slide

Evaluation of definite integrals

Question

The difference between the greatest and least values of the function $F (x) = \int_{0}^{x} (t + 1) d t on [1, 3]$ is

Moderate

A

8
B

2
C

6
D

$11 / 2$

Solution

$F^{'} (x) = x + 1 > 0 for x \in [1, 3]$ Therefore, the greatest value is F(3) and the least value is F(1). The required difference is $\int_{0}^{3} (t + 1) d t - \int_{0}^{1} (t + 1) d t = \int_{1}^{3} (t + 1) d t = 6 .$

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