What is the integral from 0 to 2 of sqrt(5+x) ?

The integral from 0 to 2 of sqrt(5+x) is (14sqrt(7)-10sqrt(5))/3

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integral from 0 to 2 of sqrt(5+x)

\int_{0}^{2} 5 + x d x

\frac{14 7 - 10 5}{3}

Decimal

4.89327 \dots

Solution steps

\int_{0}^{2} 5 + x d x

Apply u-substitution

: \int_{5}^{7} u d u

= \int_{5}^{7} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{7}

= [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{7}

Compute the boundaries:

\frac{14 7 - 10 5}{3}

= \frac{14 7 - 10 5}{3}

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What is the integral from 0 to 2 of sqrt(5+x) ?
The integral from 0 to 2 of sqrt(5+x) is (14sqrt(7)-10sqrt(5))/3