What is the integral from 0 to 4 of sqrt(x+5) ?

The integral from 0 to 4 of sqrt(x+5) is 18-(10sqrt(5))/3

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integral from 0 to 4 of sqrt(x+5)

\int_{0}^{4} x + 5 d x

18 - \frac{10 5}{3}

Decimal

10.54644 \dots

Solution steps

\int_{0}^{4} x + 5 d x

Apply u-substitution

: \int_{5}^{9} u d u

= \int_{5}^{9} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{9}

= [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{9}

Compute the boundaries:

18 - \frac{10 5}{3}

= 18 - \frac{10 5}{3}

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What is the integral from 0 to 4 of sqrt(x+5) ?
The integral from 0 to 4 of sqrt(x+5) is 18-(10sqrt(5))/3