JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

Let

f\left( x \right) = \int \,\,\frac{{{x^2}\,dx}}{{\left( {1 + {x^2}} \right)\,\,\left( {1 + \sqrt {1 + {x^2}} } \right)}}

and

f\left( 0 \right) = 0

. Then,

f\left( 1 \right)

View answer and explanation

Correct option: B

\log \,\,\left( {1 + \sqrt 2 } \right)\,\, - \,\,\frac{\pi }{4}

Option B (

\log \\,\left( {1\\ + \\,\sqrt 2 } \right)\\,\\ - \\,\\,\frac{\pi }{4}

) is correct because after solving the integral and applying the given condition

f(0) = 0

, we find that

f(1) = \log \\,\left( {1\\ + \\,\sqrt 2 } \right)\\,\\ - \\,\\,\frac{\pi }{4}

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