What is the integral from 2 to 11 of (x-3)^{-2/3} ?

The integral from 2 to 11 of (x-3)^{-2/3} is 9

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integral from 2 to 11 of (x-3)^{-2/3}

\int_{2}^{11} (x - 3)^{- \frac{2}{3}} d x

9

Solution steps

\int_{2}^{11} (x - 3)^{- \frac{2}{3}} d x

Find undefined (singularity) points:

x = 3

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_{2}^{3} (x - 3)^{- \frac{2}{3}} d x + \int_{3}^{11} (x - 3)^{- \frac{2}{3}} d x

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

\int_{3}^{11} (x - 3)^{- \frac{2}{3}} d x = 6

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

Simplify

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

= 9

f (x) = arcsin (3 x)

∣ sin (x) ∣

n = 4 \sum \infty (\frac{1}{4})^{n}

\int \frac{2 x + 3}{( x - 3 ) ( x + 3 )} d x

\frac{\partial}{\partial x} (tan (y) e^{x})

What is the integral from 2 to 11 of (x-3)^{-2/3} ?
The integral from 2 to 11 of (x-3)^{-2/3} is 9