What is the integral from 0 to 5 of sqrt(x+1) ?

The integral from 0 to 5 of sqrt(x+1) is 4sqrt(6)-2/3

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integral from 0 to 5 of sqrt(x+1)

\int_{0}^{5} x + 1 d x

46 - \frac{2}{3}

Decimal Notation

9.13129 \dots

Solution steps

\int_{0}^{5} x + 1 d x

Apply u-substitution

: \int_{1}^{6} u d u

= \int_{1}^{6} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{6}

= [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{6}

Compute the boundaries:

46 - \frac{2}{3}

= 46 - \frac{2}{3}

\int_{0}^{y} x^{2} d x

\int_{1}^{4} (1 + \frac{1}{u} + \frac{1}{u ^{2}}) d u

\int_{1}^{0} x^{3} d x

\int_{0}^{2} 2 x x^{2} - 3 x + 2 d x

\int_{- 3}^{5} x^{2} d x

What is the integral from 0 to 5 of sqrt(x+1) ?
The integral from 0 to 5 of sqrt(x+1) is 4sqrt(6)-2/3