Mathematics

# If $\displaystyle f(x)=p(x)q(x)$ where $p(x)=\sqrt{cos\:x},g(x)=log\left(\frac{(1-x)}{1+x}\right)$ the $\displaystyle \int_{a}^{b}\:f(x)\:dx$ equals where $a=-1/2,b=1/2$

$0$

##### SOLUTION
$p(x)=\sqrt{cos\:x}$
$p(-x)=\sqrt{cos\:x}=p(x)\therefore p(x)$ is an even function
$\displaystyle q(x)=log\left(\frac{1+x}{1-x}\right)$
$\displaystyle q(-x)=log\left(\frac{1-x}{1+x}\right)=-q(x)\therefore q(x)$ is an odd function
Now $f(x)=p(x)q(x)=$ Product of even and odd function
=an odd function
$\displaystyle \therefore \int_{a}^{b}f(x)f(x)dx$  is equal 0, as a,b  are opposite in sign equal in magnitude

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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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