What is the integral from 0 to 4 of sqrt(x+1) ?

The integral from 0 to 4 of sqrt(x+1) is (10sqrt(5)-2)/3

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integral from 0 to 4 of sqrt(x+1)

\int_{0}^{4} x + 1 d x

\frac{10 5 - 2}{3}

Decimal

6.78689 \dots

Solution steps

\int_{0}^{4} x + 1 d x

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

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

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What is the integral from 0 to 4 of sqrt(x+1) ?
The integral from 0 to 4 of sqrt(x+1) is (10sqrt(5)-2)/3