What is the integral from-1 to 64 of 1/(x^{1/3)} ?

The integral from-1 to 64 of 1/(x^{1/3)} is 45/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 64 of 1/(x^{1/3)}

\int_{- 1}^{64} \frac{1}{x ^{\frac{1}{3}}} d x

\frac{45}{2}

Decimal Notation

22.5

Solution steps

\int_{- 1}^{64} \frac{1}{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_{- 1}^{0} \frac{1}{x ^{\frac{1}{3}}} d x + \int_{0}^{64} \frac{1}{x ^{\frac{1}{3}}} d x

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

\int_{0}^{64} \frac{1}{x ^{\frac{1}{3}}} d x = 24

= - \frac{3 ( - 1 ) ^{\frac{2}{3}}}{2} + 24

Simplify

- \frac{3 ( - 1 ) ^{\frac{2}{3}}}{2} + 24 : \frac{45}{2}

= \frac{45}{2}

n = 1 \sum \infty \frac{2}{3 ^{n}}

x \to 2 lim (3 + 2 x + x^{2})

x \to 3 lim (\frac{∣ x - 3 ∣}{x + 3})

f (x) = 16 - 7 e^{x}

\int sin (a) x d x

What is the integral from-1 to 64 of 1/(x^{1/3)} ?
The integral from-1 to 64 of 1/(x^{1/3)} is 45/2