What is the integral from-4 to 0 of 1/((x+2)^{1/3)} ?

The integral from-4 to 0 of 1/((x+2)^{1/3)} is 0

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integral from-4 to 0 of 1/((x+2)^{1/3)}

\int_{- 4}^{0} \frac{1}{( x + 2 ) ^{\frac{1}{3}}} d x

0

Solution steps

\int_{- 4}^{0} \frac{1}{( x + 2 ) ^{\frac{1}{3}}} d x

Find undefined (singularity) points:

x = - 2

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_{- 4}^{- 2} \frac{1}{( x + 2 ) ^{\frac{1}{3}}} d x + \int_{- 2}^{0} \frac{1}{( x + 2 ) ^{\frac{1}{3}}} d x

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

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

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

Simplify

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

= 0

\frac{d}{d x} (\frac{( 6 e ^{x} )}{2 e ^{x} + 1})

\frac{1}{2 x}, at x = 64

\int \frac{1}{x 121 x ^{2} - 121} d x

\int y + x d x

x \to 3 lim (\frac{∣ 3 - x ∣}{x - 3})

What is the integral from-4 to 0 of 1/((x+2)^{1/3)} ?
The integral from-4 to 0 of 1/((x+2)^{1/3)} is 0