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

The integral from-1 to 3 of 1/(\sqrt[3]{x)} is -3/2+(3*3^{2/3})/2

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

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

- \frac{3}{2} + \frac{3 \cdot 3 ^{\frac{2}{3}}}{2}

Decimal

1.62012 \dots

Solution steps

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

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

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

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

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

= - \frac{3}{2} + \frac{3 \cdot 3 ^{\frac{2}{3}}}{2}

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What is the integral from-1 to 3 of 1/(\sqrt[3]{x)} ?
The integral from-1 to 3 of 1/(\sqrt[3]{x)} is -3/2+(3*3^{2/3})/2