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

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

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

3 \cdot 4^{\frac{1}{3}} + 3 \cdot 2^{\frac{1}{3}}

Decimal

8.54196 \dots

Solution steps

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

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

Simplify

- 3 (- 1)^{\frac{1}{3}} \cdot 4^{\frac{1}{3}} + 3 \cdot 2^{\frac{1}{3}} : 3 \cdot 4^{\frac{1}{3}} + 3 \cdot 2^{\frac{1}{3}}

= 3 \cdot 4^{\frac{1}{3}} + 3 \cdot 2^{\frac{1}{3}}

\int_{- 1}^{0} 3 x^{3} d x

\int_{1}^{4} 2 x + \frac{1}{x} d x

\int_{- 1}^{1} 3 x^{2} + 5 d x

\int_{0}^{1} (1 - t)^{2} d t

\int_{- 1}^{1} \frac{5}{1 + 25 t ^{2}} d t

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