What is the integral from 0 to 64 of 5/(x^{2/3)} ?

The integral from 0 to 64 of 5/(x^{2/3)} is 60

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integral from 0 to 64 of 5/(x^{2/3)}

\int_{0}^{64} \frac{5}{x ^{\frac{2}{3}}} d x

60

Solution steps

\int_{0}^{64} \frac{5}{x ^{\frac{2}{3}}} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{64} \frac{1}{x ^{\frac{2}{3}}} d x

Apply the Power Rule

= 5 [3 x^{\frac{1}{3}}]_{0}^{64}

Compute the boundaries:

12

= 5 \cdot 12

Simplify

= 60

What is the integral from 0 to 64 of 5/(x^{2/3)} ?
The integral from 0 to 64 of 5/(x^{2/3)} is 60