What is the integral from 0 to 5 of 7*\sqrt[3]{x^2} ?

The integral from 0 to 5 of 7*\sqrt[3]{x^2} is 21*5^{2/3}

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integral from 0 to 5 of 7*\sqrt[3]{x^2}

\int_{0}^{5} 7 \cdot 3 x^{2} d x

21 \cdot 5^{\frac{2}{3}}

Decimal

61.40437 \dots

Solution steps

\int_{0}^{5} 7 3 x^{2} d x

Take the constant out:

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

= 7 \cdot \int_{0}^{5} 3 x^{2} d x

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

assuming

x \geq 0

= 7 \cdot \int_{0}^{5} x^{\frac{2}{3}} d x

Apply the Power Rule

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

= 7 [\frac{3}{5} x^{\frac{5}{3}}]_{0}^{5}

Compute the boundaries:

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

= 7 \cdot 3 \cdot 5^{\frac{2}{3}}

Simplify

= 21 \cdot 5^{\frac{2}{3}}

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What is the integral from 0 to 5 of 7*\sqrt[3]{x^2} ?
The integral from 0 to 5 of 7*\sqrt[3]{x^2} is 21*5^{2/3}