What is the integral from 0 to 6 of sqrt(6x) ?

The integral from 0 to 6 of sqrt(6x) is 24

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integral from 0 to 6 of sqrt(6x)

\int_{0}^{6} 6 x d x

24

Solution steps

\int_{0}^{6} 6 x d x

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \int_{0}^{6} 6 x d x

Take the constant out:

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

= 6 \cdot \int_{0}^{6} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{6}

= 6 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{6}

Compute the boundaries:

46

= 6 \cdot 46

Simplify

= 24

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What is the integral from 0 to 6 of sqrt(6x) ?
The integral from 0 to 6 of sqrt(6x) is 24