What is the integral from 0 to 8 of sqrt(2x) ?

The integral from 0 to 8 of sqrt(2x) is 64/3

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integral from 0 to 8 of sqrt(2x)

\int_{0}^{8} 2 x d x

\frac{64}{3}

Decimal Notation

21.33333 \dots

Solution steps

\int_{0}^{8} 2 x d x

Apply Integration By Parts

: [2 x x - \int \frac{x}{2} d x]_{0}^{8}

= [2 x x - \int \frac{x}{2} d x]_{0}^{8}

\int \frac{x}{2} d x = \frac{2}{3} x^{\frac{3}{2}}

= [2 x x - \frac{2}{3} x^{\frac{3}{2}}]_{0}^{8}

Compute the boundaries:

\frac{64}{3}

= \frac{64}{3}

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What is the integral from 0 to 8 of sqrt(2x) ?
The integral from 0 to 8 of sqrt(2x) is 64/3