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

The integral from 0 to 4 of 1/((x-2)^{2/3)} is 6*2^{1/3}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

6 \cdot 2^{\frac{1}{3}}

Decimal Notation

7.55952 \dots

Solution steps

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

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

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

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

Simplify

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

= 6 \cdot 2^{\frac{1}{3}}

\int_{\frac{π}{4}}^{π} cot (x) d x

\int_{0}^{1} π (x - x^{2})^{2} d x

\int_{0}^{\infty} e^{x} sin (x) d x

\int_{0}^{4} 4 x^{3} d x

\int_{0}^{\frac{π}{4}} cos^{3} (2 x) d x

What is the integral from 0 to 4 of 1/((x-2)^{2/3)} ?
The integral from 0 to 4 of 1/((x-2)^{2/3)} is 6*2^{1/3}