If $n \in N$, then $\int_\limits 0^n(x-[x]) d x$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

n \in N

, then

\int\limits_{0}^n(x-[x]) d x

is equal to

View answer and explanation

Correct option: B

n / 2

Option B is correct because the function

x-[x]

is periodic with period 1, so the integral simplifies to

n \int_0^1 x dx = n/2

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