What is the integral from 0 to 2 of sqrt(x+1) ?

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

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integral from 0 to 2 of sqrt(x+1)

\int_{0}^{2} x + 1 d x

23 - \frac{2}{3}

Decimal

2.79743 \dots

Solution steps

\int_{0}^{2} x + 1 d x

Apply u-substitution

= \int_{1}^{3} u d u

Apply the Power Rule

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

Compute the boundaries:

23 - \frac{2}{3}

= 23 - \frac{2}{3}

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