What is the integral from 0 to 9 of sqrt(9x) ?

The integral from 0 to 9 of sqrt(9x) is 54

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integral from 0 to 9 of sqrt(9x)

\int_{0}^{9} 9 x d x

54

Solution steps

\int_{0}^{9} 9 x d x

Simplify

9 x : 3 x

= \int_{0}^{9} 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}^{9} x d x

Apply the Power Rule

= 3 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{9}

Compute the boundaries:

18

= 3 \cdot 18

Simplify

= 54

What is the integral from 0 to 9 of sqrt(9x) ?
The integral from 0 to 9 of sqrt(9x) is 54