What is the integral from 1 to 6 of 5+sqrt(x) ?

The integral from 1 to 6 of 5+sqrt(x) is 4sqrt(6)+73/3

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integral from 1 to 6 of 5+sqrt(x)

\int_{1}^{6} 5 + x d x

46 + \frac{73}{3}

Decimal

34.13129 \dots

Solution steps

\int_{1}^{6} 5 + 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}^{6} 5 d x + \int_{1}^{6} x d x

\int_{1}^{6} 5 d x = 25

\int_{1}^{6} x d x = 46 - \frac{2}{3}

= 25 + 46 - \frac{2}{3}

Combine the fractions

25 - \frac{2}{3} : \frac{73}{3}

= 46 + \frac{73}{3}

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What is the integral from 1 to 6 of 5+sqrt(x) ?
The integral from 1 to 6 of 5+sqrt(x) is 4sqrt(6)+73/3