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

The integral from 1 to 8 of 8x^{1/3} is 90

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

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

90

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{45}{4}

= 8 \cdot \frac{45}{4}

Simplify

= 90

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

\int_{2}^{6} 2 d x

\int_{- 2 π}^{2 π} 8 sin (x) d x

\int_{π}^{2 π} sin^{2} (θ) d θ

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

What is the integral from 1 to 8 of 8x^{1/3} ?
The integral from 1 to 8 of 8x^{1/3} is 90