What is the integral from 1 to n of ([x])/x ?

The integral from 1 to n of ([x])/x is n-1

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integral from 1 to n of ([x])/x

\int_{1}^{n} \frac{[ x ]}{x} d x

n - 1

Solution steps

\int_{1}^{n} \frac{[ x ]}{x} d x

Simplify

= \int_{1}^{n} 1 d x

Integral of a constant:

\int a d x = a x

= [1 \cdot x]_{1}^{n}

Simplify

= [x]_{1}^{n}

Compute the boundaries:

n - 1

= n - 1

\int_{0}^{2} x^{\frac{3}{2}} d x

\int_{1}^{1} 3 x d x

\int_{0}^{x} cos (t) d t

\int_{0}^{2} 5 t cos (π \cdot t) d t

\int_{9}^{16} 8 x d x

What is the integral from 1 to n of ([x])/x ?
The integral from 1 to n of ([x])/x is n-1