What is the integral from 0 to 4 of (5+7sqrt(x)) ?

The integral from 0 to 4 of (5+7sqrt(x)) is 172/3

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integral from 0 to 4 of (5+7sqrt(x))

\int_{0}^{4} (5 + 7 x) d x

\frac{172}{3}

Decimal Notation

57.33333 \dots

Solution steps

\int_{0}^{4} 5 + 7 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_{0}^{4} 5 d x + \int_{0}^{4} 7 x d x

\int_{0}^{4} 5 d x = 20

\int_{0}^{4} 7 x d x = \frac{112}{3}

= 20 + \frac{112}{3}

Simplify

20 + \frac{112}{3} : \frac{172}{3}

= \frac{172}{3}

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What is the integral from 0 to 4 of (5+7sqrt(x)) ?
The integral from 0 to 4 of (5+7sqrt(x)) is 172/3