What is the integral from-1 to 1 of 1/(x^{4/5)} ?

The integral from-1 to 1 of 1/(x^{4/5)} is 10

Popular >

integral from-1 to 1 of 1/(x^{4/5)}

\int_{- 1}^{1} \frac{1}{x ^{\frac{4}{5}}} d x

10

Solution steps

\int_{- 1}^{1} \frac{1}{x ^{\frac{4}{5}}} 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}{x ^{\frac{4}{5}}} d x + \int_{0}^{1} \frac{1}{x ^{\frac{4}{5}}} d x

\int_{- 1}^{0} \frac{1}{x ^{\frac{4}{5}}} d x = - 5 (- 1)^{\frac{1}{5}}

\int_{0}^{1} \frac{1}{x ^{\frac{4}{5}}} d x = 5

= - 5 (- 1)^{\frac{1}{5}} + 5

Simplify

- 5 (- 1)^{\frac{1}{5}} + 5 : 10

= 10

f (x) = (\frac{- 7}{7 x ^{2} + 1})

x \to 2 lim (\frac{2 + x}{x - 2})

x - 2 x^{2}, - 5 x

y^{^{'}} = t y^{3} - y

x \to - 2 lim ((3 x^{2}) - 6 x + 2)

What is the integral from-1 to 1 of 1/(x^{4/5)} ?
The integral from-1 to 1 of 1/(x^{4/5)} is 10