What is the integral from 0 to 16 of (2sqrt(x)) ?

The integral from 0 to 16 of (2sqrt(x)) is 256/3

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integral from 0 to 16 of (2sqrt(x))

\int_{0}^{16} (2 x) d x

\frac{256}{3}

Decimal

85.33333 \dots

Solution steps

\int_{0}^{16} 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}^{16} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{16}

= 2 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{16}

Compute the boundaries:

\frac{128}{3}

= 2 \cdot \frac{128}{3}

Simplify

= \frac{256}{3}

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What is the integral from 0 to 16 of (2sqrt(x)) ?
The integral from 0 to 16 of (2sqrt(x)) is 256/3