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

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

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

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

\frac{10 5 - 4 2}{3}

Decimal

5.56794 \dots

Solution steps

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

Apply u-substitution

: \int_{2}^{5} u d u

= \int_{2}^{5} u d u

Apply the Power Rule

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

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

Compute the boundaries:

\frac{10 5 - 4 2}{3}

= \frac{10 5 - 4 2}{3}

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