What is the integral from 0 to 9 of 5sqrt(x) ?

The integral from 0 to 9 of 5sqrt(x) is 90

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integral from 0 to 9 of 5sqrt(x)

\int_{0}^{9} 5 x d x

90

Solution steps

\int_{0}^{9} 5 x d x

Take the constant out:

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

= 5 \cdot \int_{0}^{9} x d x

Apply the Power Rule

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

= 5 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{9}

Compute the boundaries:

18

= 5 \cdot 18

Simplify

= 90

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What is the integral from 0 to 9 of 5sqrt(x) ?
The integral from 0 to 9 of 5sqrt(x) is 90