What is the integral from 8 to infinity of x^{-4/3} ?

The integral from 8 to infinity of x^{-4/3} is 3/2

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integral from 8 to infinity of x^{-4/3}

\int_{8}^{\infty} x^{- \frac{4}{3}} d x

\frac{3}{2}

Decimal

1.5

Solution steps

\int_{8}^{\infty} x^{- \frac{4}{3}} d x

Compute the indefinite integral:

\int x^{- \frac{4}{3}} d x = - \frac{3}{x ^{\frac{1}{3}}} + C

Compute the boundaries:

\int_{8}^{\infty} x^{- \frac{4}{3}} d x = 0 - (- \frac{3}{2})

= 0 - (- \frac{3}{2})

Simplify

= \frac{3}{2}

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What is the integral from 8 to infinity of x^{-4/3} ?
The integral from 8 to infinity of x^{-4/3} is 3/2