What is the integral from 9 to 16 of 8sqrt(x) ?

The integral from 9 to 16 of 8sqrt(x) is 592/3

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integral from 9 to 16 of 8sqrt(x)

\int_{9}^{16} 8 x d x

\frac{592}{3}

Decimal

197.33333 \dots

Solution steps

\int_{9}^{16} 8 x d x

Take the constant out:

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

= 8 \cdot \int_{9}^{16} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{9}^{16}

= 8 [\frac{2}{3} x^{\frac{3}{2}}]_{9}^{16}

Compute the boundaries:

\frac{74}{3}

= 8 \cdot \frac{74}{3}

Simplify

= \frac{592}{3}

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What is the integral from 9 to 16 of 8sqrt(x) ?
The integral from 9 to 16 of 8sqrt(x) is 592/3