What is the integral from 1 to 8 of 2/(x^{1/3)} ?

The integral from 1 to 8 of 2/(x^{1/3)} is 9

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integral from 1 to 8 of 2/(x^{1/3)}

\int_{1}^{8} \frac{2}{x ^{\frac{1}{3}}} d x

9

Solution steps

\int_{1}^{8} \frac{2}{x ^{\frac{1}{3}}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{1}^{8} \frac{1}{x ^{\frac{1}{3}}} d x

Apply the Power Rule

: [\frac{3}{2} x^{\frac{2}{3}}]_{1}^{8}

= 2 [\frac{3}{2} x^{\frac{2}{3}}]_{1}^{8}

Compute the boundaries:

\frac{9}{2}

= 2 \cdot \frac{9}{2}

Simplify

= 9

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What is the integral from 1 to 8 of 2/(x^{1/3)} ?
The integral from 1 to 8 of 2/(x^{1/3)} is 9