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

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

Popular >

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

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

12

Solution steps

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

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

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

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

Simplify

- \frac{3 ( - 1 ) ^{\frac{2}{3}}}{2} + \frac{27}{2} : 12

= 12

\int_{0}^{6} - 3 x^{2} - 9 x + 162 d x

\int_{- 1}^{5} (3 x^{2} + 4 x) d x

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

\int_{0}^{2 π} 3 sin (t) cos (t) d t

\int_{a}^{b} x^{- 2} d x

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