$\int_{0}^{1}{\left( \left\{ x \right\}\lbrack x + 1\rbrack \right)dx}$ (where $\{ \bullet \}$ denotes fractional part of $x$ and $\lbrack \bullet \rbrack$ denotes greatest integer of $x)$ is equal to

Question

Dr. Abubacker · Accepted Answer

(c)
$\left\{ x ight\} = x$ when $0 < x < 1$ and $\lbrack x + 1brack = 1$
$	herefore\ \int_{0}^{1}{\left( \left\{ x ight\}\lbrack x + 1brack ight)dx =}\int_{0}^{1}{x\ dx = \frac{1}{2}}$

Q. $\int_{0}^{1}{\left( \left\{ x \right\}\lbrack x + 1\rbrack \right)dx}$ (where $\{ \bullet \}$ denotes fractional part of $x$ and $\lbrack \bullet \rbrack$ denotes greatest integer of $x)$ is equal to

Explanation

Reviewed by Dr. Abubacker

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