What is the integral from 0 to 8 of pix^{2/3} ?

The integral from 0 to 8 of pix^{2/3} is (96pi)/5

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integral from 0 to 8 of pix^{2/3}

\int_{0}^{8} π x^{\frac{2}{3}} d x

\frac{96 π}{5}

Decimal

60.31857 \dots

Solution steps

\int_{0}^{8} π x^{\frac{2}{3}} d x

Take the constant out:

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

= π \cdot \int_{0}^{8} x^{\frac{2}{3}} d x

Apply the Power Rule

: [\frac{3}{5} x^{\frac{5}{3}}]_{0}^{8}

= π [\frac{3}{5} x^{\frac{5}{3}}]_{0}^{8}

Compute the boundaries:

\frac{96}{5}

= π \frac{96}{5}

Simplify

= \frac{96 π}{5}

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What is the integral from 0 to 8 of pix^{2/3} ?
The integral from 0 to 8 of pix^{2/3} is (96pi)/5