What is the integral from 1 to infinity of x^{-8} ?

The integral from 1 to infinity of x^{-8} is 1/7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to infinity of x^{-8}

\int_{1}^{\infty} x^{- 8} d x

\frac{1}{7}

Decimal

0.14285 \dots

Solution steps

\int_{1}^{\infty} x^{- 8} d x

Compute the indefinite integral:

\int x^{- 8} d x = - \frac{1}{7 x ^{7}} + C

Compute the boundaries:

\int_{1}^{\infty} x^{- 8} d x = 0 - (- \frac{1}{7})

= 0 - (- \frac{1}{7})

Simplify

= \frac{1}{7}

e^{x}, 2 x - 1, x = 1, x = 2

x \to 1 - lim (\frac{x + 1}{x ^{2} - 1})

f (x) = (x^{2} - 10)^{4}

\int_{0}^{π} (1 - cos^{2} (x)) d x

h \to 0 lim (h^{4})

What is the integral from 1 to infinity of x^{-8} ?
The integral from 1 to infinity of x^{-8} is 1/7