What is the integral from 1/2 to 1 of x^3[ 1/x ] ?

The integral from 1/2 to 1 of x^3[ 1/x ] is 7/24

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integral from 1/2 to 1 of x^3[ 1/x ]

\int_{\frac{1}{2}}^{1} x^{3} [\frac{1}{x}] d x

\frac{7}{24}

Decimal

0.29166 \dots

Solution steps

\int_{\frac{1}{2}}^{1} x^{3} [\frac{1}{x}] d x

Simplify

x^{3} [\frac{1}{x}] : x^{2}

= \int_{\frac{1}{2}}^{1} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{\frac{1}{2}}^{1}

= [\frac{x ^{3}}{3}]_{\frac{1}{2}}^{1}

Compute the boundaries:

\frac{7}{24}

= \frac{7}{24}

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What is the integral from 1/2 to 1 of x^3[ 1/x ] ?
The integral from 1/2 to 1 of x^3[ 1/x ] is 7/24