What is the integral from 0 to 9 of sqrt(4x) ?

The integral from 0 to 9 of sqrt(4x) is 36

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integral from 0 to 9 of sqrt(4x)

\int_{0}^{9} 4 x d x

36

Solution steps

\int_{0}^{9} 4 x d x

Simplify

4 x : 2 x

= \int_{0}^{9} 2 x d x

Take the constant out:

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

= 2 \cdot \int_{0}^{9} x d x

Apply the Power Rule

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

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

Compute the boundaries:

18

= 2 \cdot 18

Simplify

= 36

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What is the integral from 0 to 9 of sqrt(4x) ?
The integral from 0 to 9 of sqrt(4x) is 36