Let $f\,\,\left( x \right) = x\,\, - \,\,\left[ x \right]$, for every real number $x$, where $\left[ x \right]$ is the integral part of $x$. Then, $\mathop \smallint \nolimits_{ - 1}^1 \,\,f\,\,\left( x \right)\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Let

f\,\,\left( x \right) = x\,\, - \,\,\left[ x \right]

, for every real number

x

, where

\left[ x \right]

is the integral part of

x

. Then,

\int \nolimits_{ - 1}^1 \,\,f\,\,\left( x \right)\,\,dx

is equal to

View answer and explanation

Correct option: A

1

Option A (1) is correct because the integral of the fractional part of x over the given interval is equal to 1.

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