If $f\left( x \right) = \mathop \smallint \nolimits_{ - 1}^x \,\,\left| {\,t\,} \right|\,\,dt$, then for any $x \ge 0,\,\,f\left( x \right)$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f\left( x \right) = \int \nolimits_{ - 1}^x \,\,\left| {\,t\,} \right|\,\,dt

, then for any

x \ge 0,\,\,f\left( x \right)

is equal to

View answer and explanation

Correct option: B

\frac{1}{2}\,\,\left( {1\,\, + \,\,{x^2}} \right)

Option B is correct because the integral of the absolute value function is split into two parts and then evaluated.

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