Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

The solution for $x$ of the equation $\int_{\sqrt{2}}^{x}\; \frac{dt}{t\sqrt{t^{2}-1}}=\frac{\pi }{2}$ is

Option 1)
$\frac{\sqrt{3}}{2}\;$

Option 2)
$\; 2\sqrt{2}\;$

Option 3)
$\; 2\;$

Option 4)
$\; \pi$

Answers (1)

best_answer

As learnt in cocept

Integration of Rational and irrational function -

Integration in the form of :

(i) $\int \frac{dx}{x^{2}+a^{2}}$ (ii) $\int \frac{dx}{x^{2}-a^{2}}$ (iii) $\int \frac{dx}{a^{2}-x^{2}}$

(iv) $\int \frac{dx}{\sqrt{x^{2}+a^{2}}}$ (v) $\frac{dx}{\sqrt{x^{2}-a^{2}}}$ (vi) $\frac{dx}{\sqrt{a^{2}-x^{2}}}$

-

$A=\int_{\sqrt{2}}^{x}\frac{dt}{t\sqrt{t^2 -1 }} =[sec^{-1}t]^x_{\sqrt{2}}$

As per the formula of integration

Given $[sec^{-1}t]^x_{\sqrt{2}} = \frac{\pi }{2}$

$sec^{-1}x-{sec^{-1}\sqrt{2}} = \frac{\pi }{2}$

$sec^{-1}x = \frac{\pi }{2}+ \frac{\pi }{4} = \frac{3\pi}{4}$

$x = sec\frac{3\pi }{4} =\:-\sqrt{2}$

Option 1)

$\frac{\sqrt{3}}{2}\;$

Option 2)

$\; 2\sqrt{2}\;$

Option 3)

$\; 2\;$

Option 4)

$\; \pi$

Posted by

prateek

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE aspirant in Kota commits suicide; 16th suicide since January

anam-khan

JEE Main 2025 Registration Live: NTA session 1 application last date today; official website, syllabus

anam-khan

JEE Main 2025 session 1 registration ends today at jeemain.nta.nic.in; application correction from November 26

Latest Question