Let $f\,\,\left( x \right) = \smallint \,\,\frac{1}{{{{\left( {1 + {x^2}} \right)}^{3/2}}}}\,\,dx$ and $f\,\,\left( 0 \right) = 0$, then $f\,\,\left( 1 \right) = $

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

Let

f\,\,\left( x \right) = \int \,\,\frac{1}{{{{\left( {1 + {x^2}} \right)}^{3/2}}}}\,\,dx

and

f\,\,\left( 0 \right) = 0

, then

f\,\,\left( 1 \right) =

View answer and explanation

Correct option: B

\frac{1}{{\sqrt 2 }}

Option B (

\frac{1}{{\sqrt 2 }}

) is correct because the integral of the given function is evaluated, and the constant of integration is determined using the initial condition f(0) = 0.

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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