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

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

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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}

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