What is the integral from-8 to 27 of 1/(x^{1/3)} ?

The integral from-8 to 27 of 1/(x^{1/3)} is 15/2

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integral from-8 to 27 of 1/(x^{1/3)}

\int_{- 8}^{27} \frac{1}{x ^{\frac{1}{3}}} d x

\frac{15}{2}

Decimal

7.5

Solution steps

\int_{- 8}^{27} \frac{1}{x ^{\frac{1}{3}}} d x

Find undefined (singularity) points:

x = 0

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 8}^{0} \frac{1}{x ^{\frac{1}{3}}} d x + \int_{0}^{27} \frac{1}{x ^{\frac{1}{3}}} d x

\int_{- 8}^{0} \frac{1}{x ^{\frac{1}{3}}} d x = - 6 (- 1)^{\frac{2}{3}}

\int_{0}^{27} \frac{1}{x ^{\frac{1}{3}}} d x = \frac{27}{2}

= - 6 (- 1)^{\frac{2}{3}} + \frac{27}{2}

Simplify

- 6 (- 1)^{\frac{2}{3}} + \frac{27}{2} : \frac{15}{2}

= \frac{15}{2}

What is the integral from-8 to 27 of 1/(x^{1/3)} ?
The integral from-8 to 27 of 1/(x^{1/3)} is 15/2