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

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

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

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

\frac{16}{3}

Decimal

5.33333 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

\frac{8}{3}

= 2 \cdot \frac{8}{3}

Simplify

= \frac{16}{3}

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