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

The integral from-27 to 1 of 1/(x^{2/3)} is 12

Popular >

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

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

12

Solution steps

\int_{- 27}^{1} \frac{1}{x ^{\frac{2}{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_{- 27}^{0} \frac{1}{x ^{\frac{2}{3}}} d x + \int_{0}^{1} \frac{1}{x ^{\frac{2}{3}}} d x

\int_{- 27}^{0} \frac{1}{x ^{\frac{2}{3}}} d x = - 9 (- 1)^{\frac{1}{3}}

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

= - 9 (- 1)^{\frac{1}{3}} + 3

Simplify

- 9 (- 1)^{\frac{1}{3}} + 3 : 12

= 12

\int_{0}^{1} (1 + x)^{4} d x

\int_{1}^{11} \frac{1}{( x - 3 ) ^{\frac{2}{3}}} d x

\int_{- \infty}^{- 1} θ e^{θ} d θ

\int_{0}^{1} (π x) d x

\int_{0}^{1} \frac{1 - x}{x} d x

What is the integral from-27 to 1 of 1/(x^{2/3)} ?
The integral from-27 to 1 of 1/(x^{2/3)} is 12