What is the integral from 1 to 4 of 9x^{-3/2} ?

The integral from 1 to 4 of 9x^{-3/2} is 9

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integral from 1 to 4 of 9x^{-3/2}

\int_{1}^{4} 9 x^{- \frac{3}{2}} d x

9

Solution steps

\int_{1}^{4} 9 x^{- \frac{3}{2}} d x

Take the constant out:

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

= 9 \cdot \int_{1}^{4} x^{- \frac{3}{2}} d x

Apply the Power Rule

: [- \frac{2}{x ^{\frac{1}{2}}}]_{1}^{4}

= 9 [- \frac{2}{x ^{\frac{1}{2}}}]_{1}^{4}

Compute the boundaries:

1

= 9 \cdot 1

Simplify

= 9

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What is the integral from 1 to 4 of 9x^{-3/2} ?
The integral from 1 to 4 of 9x^{-3/2} is 9