What is the integral from 1 to R of x^{-8/5} ?

The integral from 1 to R of x^{-8/5} is -5/(3R^{3/5)}+5/3

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integral from 1 to R of x^{-8/5}

\int_{1}^{R} x^{- \frac{8}{5}} d x

- \frac{5}{3 R ^{\frac{3}{5}}} + \frac{5}{3}

Solution steps

\int_{1}^{R} x^{- \frac{8}{5}} d x

Apply the Power Rule

: [- \frac{5}{3 x ^{\frac{3}{5}}}]_{1}^{R}

= [- \frac{5}{3 x ^{\frac{3}{5}}}]_{1}^{R}

Compute the boundaries:

- \frac{5}{3 R ^{\frac{3}{5}}} + \frac{5}{3}

= - \frac{5}{3 R ^{\frac{3}{5}}} + \frac{5}{3}

\int x^{0} d x

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What is the integral from 1 to R of x^{-8/5} ?
The integral from 1 to R of x^{-8/5} is -5/(3R^{3/5)}+5/3