What is the integral from 1 to 8 of \sqrt[3]{x^2} ?

The integral from 1 to 8 of \sqrt[3]{x^2} is 93/5

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integral from 1 to 8 of \sqrt[3]{x^2}

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

\frac{93}{5}

Decimal

18.6

Solution steps

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

3 x^{2} = x^{\frac{2}{3}},

assuming

x \geq 0

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

Apply the Power Rule

= [\frac{3}{5} x^{\frac{5}{3}}]_{1}^{8}

Compute the boundaries:

\frac{93}{5}

= \frac{93}{5}

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What is the integral from 1 to 8 of \sqrt[3]{x^2} ?
The integral from 1 to 8 of \sqrt[3]{x^2} is 93/5