What is the integral from 0 to 5 of sqrt(1+x) ?

The integral from 0 to 5 of sqrt(1+x) is 4sqrt(6)-2/3

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integral from 0 to 5 of sqrt(1+x)

\int_{0}^{5} 1 + x d x

46 - \frac{2}{3}

Decimal Notation

9.13129 \dots

Solution steps

\int_{0}^{5} 1 + x d x

Apply u-substitution

: \int_{1}^{6} u d u

= \int_{1}^{6} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{6}

= [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{6}

Compute the boundaries:

46 - \frac{2}{3}

= 46 - \frac{2}{3}

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What is the integral from 0 to 5 of sqrt(1+x) ?
The integral from 0 to 5 of sqrt(1+x) is 4sqrt(6)-2/3