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

The integral from 1 to 3 of 3x^{-3/2} is 3(-2/(3^{1/2)}+2)

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

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

3 (- \frac{2}{3 ^{\frac{1}{2}}} + 2)

Decimal Notation

2.53589 \dots

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: [- \frac{2}{x ^{\frac{1}{2}}}]_{1}^{3}

= 3 [- \frac{2}{x ^{\frac{1}{2}}}]_{1}^{3}

Compute the boundaries:

- \frac{2}{3 ^{\frac{1}{2}}} + 2

= 3 (- \frac{2}{3 ^{\frac{1}{2}}} + 2)

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What is the integral from 1 to 3 of 3x^{-3/2} ?
The integral from 1 to 3 of 3x^{-3/2} is 3(-2/(3^{1/2)}+2)