For any $n \in N$ and $x \in {R^ + }$, the value of the integral $\mathop \smallint \limits_0^{n\left[ x \right]} \left( {x - \left[ x \right]} \right)dx$, is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

For any

n \in N

and

x \in {R^ + }

, the value of the integral

\int \limits_0^{n\left[ x \right]} \left( {x - \left[ x \right]} \right)dx

, is

View answer and explanation

Correct option: C

\frac{n}{2}\,\,\left[ x \right]

Option C (

\frac{n}{2}\,\,[ x ]

) is correct because the integral of the fractional part of x over one period is 1/2, and we have n[x] such periods.

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