First slide

Evaluation of definite integrals

Question

If $f (x) = \int e^{x^{2}} (x - 2) (x - 3) (x - 4) d x$
then $f$ increases on

Easy

A

$(- \infty, 2)$
B

$(2, \infty)$
C

$(2, 3)$
D

$(3, \infty)$

Solution

$f^{'} (x) = e^{x^{2}} (x - 2) (x - 3) (x - 4)$
As $e^{x^{2}} > 0$ for all $x \in R, f^{'} (x) > 0$
if $(x - 2) (x - 3) (x - 4) > 0$ i.e., if $2 < x < 3 or x > 4$
Thus $f (x)$ increases on the interval $(2, 3)$

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