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

The integral from-3 to 3 of x^{-1/3} is 0

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

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

0

Solution steps

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

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

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

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

Simplify

- \frac{3 ( - 1 ) ^{\frac{2}{3}} \cdot 3 ^{\frac{2}{3}}}{2} + \frac{3 \cdot 3 ^{\frac{2}{3}}}{2} : 0

= 0

\int_{- 1}^{2} x + 2 - x^{2} d x

x \to π lim ((x - π) csc (x))

e^{x} \frac{y d y}{d x} = e^{- y} + e^{- 2 x - y}

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

(1 - x^{2}) y^{^{''}} + 2 x y^{^{'}} = 0

What is the integral from-3 to 3 of x^{-1/3} ?
The integral from-3 to 3 of x^{-1/3} is 0