What is the integral from 1 to 8 of 4/3 x^{1/3} ?

The integral from 1 to 8 of 4/3 x^{1/3} is 15

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integral from 1 to 8 of 4/3 x^{1/3}

\int_{1}^{8} \frac{4}{3} x^{\frac{1}{3}} d x

15

Solution steps

\int_{1}^{8} \frac{4}{3} x^{\frac{1}{3}} d x

Take the constant out:

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

= \frac{4}{3} \cdot \int_{1}^{8} x^{\frac{1}{3}} d x

Apply the Power Rule

: [\frac{3}{4} x^{\frac{4}{3}}]_{1}^{8}

= \frac{4}{3} [\frac{3}{4} x^{\frac{4}{3}}]_{1}^{8}

Compute the boundaries:

\frac{45}{4}

= \frac{4}{3} \cdot \frac{45}{4}

Simplify

= 15

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What is the integral from 1 to 8 of 4/3 x^{1/3} ?
The integral from 1 to 8 of 4/3 x^{1/3} is 15