What is the integral from 0 to 2 of sqrt(1+2x) ?

The integral from 0 to 2 of sqrt(1+2x) is (5sqrt(5)-1)/3

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integral from 0 to 2 of sqrt(1+2x)

\int_{0}^{2} 1 + 2 x d x

\frac{5 5 - 1}{3}

Solution steps

\int_{0}^{2} 1 + 2 x d x

Apply u-substitution

: \int_{1}^{5} \frac{u}{2} d u

= \int_{1}^{5} \frac{u}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{5} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{5}

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{5}

Compute the boundaries:

\frac{10 5}{3} - \frac{2}{3}

= \frac{1}{2} (\frac{10 5}{3} - \frac{2}{3})

Simplify

= \frac{5 5 - 1}{3}

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What is the integral from 0 to 2 of sqrt(1+2x) ?
The integral from 0 to 2 of sqrt(1+2x) is (5sqrt(5)-1)/3