What is the integral from 1 to 3 of (x+sqrt(x)) ?

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

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integral from 1 to 3 of (x+sqrt(x))

\int_{1}^{3} (x + x) d x

23 + \frac{10}{3}

Decimal

6.79743 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{3} x d x + \int_{1}^{3} x d x

\int_{1}^{3} x d x = 4

\int_{1}^{3} x d x = 23 - \frac{2}{3}

= 4 + 23 - \frac{2}{3}

Combine the fractions

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

= 23 + \frac{10}{3}

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