What is the integral from 0 to 1 of 8\sqrt[8]{x} ?

The integral from 0 to 1 of 8\sqrt[8]{x} is 64/9

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integral from 0 to 1 of 8\sqrt[8]{x}

\int_{0}^{1} 8 8 x d x

\frac{64}{9}

Decimal

7.11111 \dots

Solution steps

\int_{0}^{1} 8 8 x d x

Take the constant out:

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

= 8 \cdot \int_{0}^{1} 8 x d x

Apply the Power Rule

: [\frac{8}{9} x^{\frac{9}{8}}]_{0}^{1}

= 8 [\frac{8}{9} x^{\frac{9}{8}}]_{0}^{1}

Compute the boundaries:

\frac{8}{9}

= 8 \cdot \frac{8}{9}

Simplify

= \frac{64}{9}

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What is the integral from 0 to 1 of 8\sqrt[8]{x} ?
The integral from 0 to 1 of 8\sqrt[8]{x} is 64/9