What is the integral from 0 to 27 of 10\sqrt[3]{x} ?

The integral from 0 to 27 of 10\sqrt[3]{x} is 1215/2

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integral from 0 to 27 of 10\sqrt[3]{x}

\int_{0}^{27} 10 3 x d x

\frac{1215}{2}

Decimal

607.5

Solution steps

\int_{0}^{27} 10 3 x d x

Take the constant out:

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

= 10 \cdot \int_{0}^{27} 3 x d x

Apply the Power Rule

: [\frac{3}{4} x^{\frac{4}{3}}]_{0}^{27}

= 10 [\frac{3}{4} x^{\frac{4}{3}}]_{0}^{27}

Compute the boundaries:

\frac{243}{4}

= 10 \cdot \frac{243}{4}

Simplify

= \frac{1215}{2}

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What is the integral from 0 to 27 of 10\sqrt[3]{x} ?
The integral from 0 to 27 of 10\sqrt[3]{x} is 1215/2