What is the integral from 0 to 27 of sqrt(3x) ?

The integral from 0 to 27 of sqrt(3x) is 162

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integral from 0 to 27 of sqrt(3x)

\int_{0}^{27} 3 x d x

162

Solution steps

\int_{0}^{27} 3 x d x

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= \int_{0}^{27} 3 x d x

Take the constant out:

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

= 3 \cdot \int_{0}^{27} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{27}

= 3 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{27}

Compute the boundaries:

543

= 3 \cdot 543

Simplify

= 162

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What is the integral from 0 to 27 of sqrt(3x) ?
The integral from 0 to 27 of sqrt(3x) is 162