What is the integral from 0 to 4 of sqrt(2x) ?

The integral from 0 to 4 of sqrt(2x) is -(8sqrt(2))/3+8sqrt(2)

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integral from 0 to 4 of sqrt(2x)

\int_{0}^{4} 2 x d x

- \frac{8 2}{3} + 82

Decimal

7.54247 \dots

Solution steps

\int_{0}^{4} 2 x d x

Apply Integration By Parts

= [2 x x - \int \frac{x}{2} d x]_{0}^{4}

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

= [2 x x - \frac{2}{3} x^{\frac{3}{2}}]_{0}^{4}

Compute the boundaries:

- 8 \cdot \frac{2}{3} + 82

= - 8 \cdot \frac{2}{3} + 82

Simplify

= - \frac{8 2}{3} + 82

What is the integral from 0 to 4 of sqrt(2x) ?
The integral from 0 to 4 of sqrt(2x) is -(8sqrt(2))/3+8sqrt(2)