What is the integral from-27 to 1 of 4/(\sqrt[3]{x)} ?

The integral from-27 to 1 of 4/(\sqrt[3]{x)} is -48

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integral from-27 to 1 of 4/(\sqrt[3]{x)}

\int_{- 27}^{1} \frac{4}{3 x} d x

- 48

Solution steps

\int_{- 27}^{1} \frac{4}{3 x} 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_{- 27}^{0} \frac{4}{3 x} d x + \int_{0}^{1} \frac{4}{3 x} d x

\int_{- 27}^{0} \frac{4}{3 x} d x = - 54 (- 1)^{\frac{2}{3}}

\int_{0}^{1} \frac{4}{3 x} d x = 6

= - 54 (- 1)^{\frac{2}{3}} + 6

Simplify

- 54 (- 1)^{\frac{2}{3}} + 6 : - 48

= - 48

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What is the integral from-27 to 1 of 4/(\sqrt[3]{x)} ?
The integral from-27 to 1 of 4/(\sqrt[3]{x)} is -48