What is the integral from 8 to 100 of 0.5x^{-1.5} ?

The integral from 8 to 100 of 0.5x^{-1.5} is 0.25355…

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integral from 8 to 100 of 0.5x^{-1.5}

\int_{8}^{100} 0.5 x^{- 1.5} d x

0.25355 \dots

Solution steps

\int_{8}^{100} 0.5 x^{- 1.5} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 0.5 \cdot \int_{8}^{100} x^{- 1.5} d x

Apply the Power Rule

= 0.5 [- \frac{2}{x}]_{8}^{100}

Compute the boundaries:

- \frac{1}{5} + \frac{1}{2}

= 0.5 (- \frac{1}{5} + \frac{1}{2})

Simplify

= 0.25355 \dots

What is the integral from 8 to 100 of 0.5x^{-1.5} ?
The integral from 8 to 100 of 0.5x^{-1.5} is 0.25355…