JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

I = \int {\frac{1}{{2p}}\sqrt {\frac{{p - 1}}{{p + 1}}} dp = f\left( p \right) + c,}

then

f\left( p \right)

is equal to

View answer and explanation

Correct option: C

\ln \sqrt {p + \sqrt {{p^2} - 1} } - \frac{1}{2}{\sec ^{ - 1}}p

Option D (None of these) is incorrect. Option C (

\ln \sqrt {p + \sqrt {{p^2} - 1} } - \frac{1}{2}{\sec ^{ - 1}}p

) is correct because after simplifying the integral, it can be split into two parts, each integrating to the terms in option C.

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