Question

Evaluate $\int_{0}^{n} [[x ]] d x$, where n is a positive integer.

Solutions

VerifiedSolution A

Solution B

Answered 1 year ago

Step 1

1 of 3$\int_{0}^{n}[x]dx=\int_{0}^{1}[x]dx+\int_{1}^{2}[x]dx+...+\int_{n-1}^{n}[x]dx$

$\int_{a}^{c}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx$

Answered 1 year ago

Step 1

1 of 6The goal of the exercise is to compute the integral

$\int_{0}^{n}\llbracket x \rrbracket\;dx$

where $\llbracket x\rrbracket$ denotes the greatest integer function.

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