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

The integral from-1 to 8 of x^{-1/3} is 9/2

Popular >

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

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

\frac{9}{2}

Decimal

4.5

Solution steps

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

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

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

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

Simplify

- \frac{3 ( - 1 ) ^{\frac{2}{3}}}{2} + 6 : \frac{9}{2}

= \frac{9}{2}

\int_{- 7}^{7} 4 x - 3 d x

\int_{0}^{3} e^{- \frac{1}{2} t} d t

\int_{- 5}^{5} \frac{7}{x ^{3}} d x

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

\int_{0}^{t} \frac{1}{1 + x ^{2}} d x

What is the integral from-1 to 8 of x^{-1/3} ?
The integral from-1 to 8 of x^{-1/3} is 9/2