If $f\left( x \right) = \mathop \smallint \limits_{ - 1}^x \,\,\left| t \right|\,\,dt$, then for any $x \ge 0,\,\,\;f\left( x \right)$ equals

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

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

, then for any

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

equals

View answer and explanation

Correct option: C

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

Option C (

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

) is correct because the integral of the absolute value function from -1 to x, for

x \ge 0

, is

\frac{1}{2}(1 + x^2)

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