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

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

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integral from 0 to 4 of (sqrt(x+2))

\int_{0}^{4} (x + 2) d x

46 - \frac{4 2}{3}

Decimal

7.91234 \dots

Solution steps

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

Apply u-substitution

: \int_{2}^{6} u d u

= \int_{2}^{6} u d u

Apply the Power Rule

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

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

Compute the boundaries:

46 - \frac{4 2}{3}

= 46 - \frac{4 2}{3}

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