What is the integral from 2 to 5 of \sqrt[3]{x^2} ?

The integral from 2 to 5 of \sqrt[3]{x^2} is 3*5^{2/3}-(6*2^{2/3})/5

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integral from 2 to 5 of \sqrt[3]{x^2}

\int_{2}^{5} 3 x^{2} d x

3 \cdot 5^{\frac{2}{3}} - \frac{6 \cdot 2 ^{\frac{2}{3}}}{5}

Decimal

6.86717 \dots

Solution steps

\int_{2}^{5} 3 x^{2} d x

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

assuming

x \geq 0

= \int_{2}^{5} x^{\frac{2}{3}} d x

Apply the Power Rule

: [\frac{3}{5} x^{\frac{5}{3}}]_{2}^{5}

= [\frac{3}{5} x^{\frac{5}{3}}]_{2}^{5}

Compute the boundaries:

3 \cdot 5^{\frac{2}{3}} - \frac{6 \cdot 2 ^{\frac{2}{3}}}{5}

= 3 \cdot 5^{\frac{2}{3}} - \frac{6 \cdot 2 ^{\frac{2}{3}}}{5}

\int_{- 2}^{- 1} cos (\frac{nπ x}{2}) d x

\int_{0}^{\frac{π}{30}} 20 cos (5 x) d x

\int_{- 3}^{5} (\frac{x}{2} + 5) d x

\int_{- 2}^{2} (6 - x^{2}) d x

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

What is the integral from 2 to 5 of \sqrt[3]{x^2} ?
The integral from 2 to 5 of \sqrt[3]{x^2} is 3*5^{2/3}-(6*2^{2/3})/5