Mathematics

# What is the value of $\int_{0}^{a}\dfrac{x-a}{x+a}\ dx$?

$a-2a\log 2$

##### SOLUTION
$I= _{0}^{a}\int \dfrac{x-a}{x+a} dx$

Let $t =x+a \Rightarrow dt =dx$

When $x= 0, t=a$

$x=a, t= 2a$

Substituting, $I= _{a}^{2a} \int \dfrac{t-2a}{t} dt$

$= [t-2a \log |t|]^{2a}_{a}$
$=2a-2a \log 2a- a+2a \log a$
$=a-2a\log 2$

$\therefore$ Option $B$ is correct.

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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