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

The integral from 0 to 8 of 2/(x^{2/3)} is 12

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integral from 0 to 8 of 2/(x^{2/3)}

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

12

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{0}^{8} \frac{1}{x ^{\frac{2}{3}}} d x

Apply the Power Rule

: [3 x^{\frac{1}{3}}]_{0}^{8}

= 2 [3 x^{\frac{1}{3}}]_{0}^{8}

Compute the boundaries:

6

= 2 \cdot 6

Simplify

= 12

\frac{d}{d x} (\frac{5}{x} - 1)

f (x) = x^{4} - 13 x^{2} + 36, at 1

\int \frac{x ^{2} - 3 x + 2}{x + 1} d x

\int \frac{5 y ^{4}}{y ^{5} - 13} d y

\frac{50 s}{s ^{2} + 25}

What is the integral from 0 to 8 of 2/(x^{2/3)} ?
The integral from 0 to 8 of 2/(x^{2/3)} is 12