First slide

Evaluation of definite integrals

Question

$\int_{1}^{3} \frac{1}{\sqrt{x + 1} - \sqrt{x - 1}} d x =$

Easy

A

$\frac{4}{3}$
B

$\frac{5}{3}$
C

$\frac{7}{3}$
D

$\frac{8}{3}$

Solution

$\int_{1}^{3} \frac{1}{\sqrt{x + 1} - \sqrt{x - 1}} d x$
$= \int_{1}^{3} \frac{\sqrt{x + 1} + \sqrt{x - 1}}{2} d x$

$= \frac{1}{2} \int_{1}^{3} (\sqrt{x + 1} + \sqrt{x - 1}) d x$

$= \frac{1}{2} \times \frac{4}{3} = \frac{8}{3}$

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