What is the integral from 0 to 4 of \sqrt[3]{x^2} ?

The integral from 0 to 4 of \sqrt[3]{x^2} is (12*4^{2/3})/5

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integral from 0 to 4 of \sqrt[3]{x^2}

\int_{0}^{4} 3 x^{2} d x

\frac{12 \cdot 4 ^{\frac{2}{3}}}{5}

Decimal

6.04762 \dots

Solution steps

\int_{0}^{4} 3 x^{2} d x

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

assuming

x \geq 0

= \int_{0}^{4} x^{\frac{2}{3}} d x

Apply the Power Rule

: [\frac{3}{5} x^{\frac{5}{3}}]_{0}^{4}

= [\frac{3}{5} x^{\frac{5}{3}}]_{0}^{4}

Compute the boundaries:

\frac{12 \cdot 4 ^{\frac{2}{3}}}{5}

= \frac{12 \cdot 4 ^{\frac{2}{3}}}{5}

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What is the integral from 0 to 4 of \sqrt[3]{x^2} ?
The integral from 0 to 4 of \sqrt[3]{x^2} is (12*4^{2/3})/5