First slide

Introduction to integration

Question

$Let f (x) = \int e^{x} (x - 1) (x - 2) d x, then f decreases in the inverval$

Moderate

A

$(- \infty, - 2)$
B

$(- 2, - 1)$
C

$(1, 2)$
D

$(2, \infty)$

Solution

$f (x) = \int e^{x} (x - 1) (x - 2) d x f^{'} (x) = e^{x} (x - 1) (x - 2) < 0 \Rightarrow x \in (1, 2)$
$since f(x) is decreasing function ⇒ f^{'} (x) < 0$

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