What is the integral from 0 to 4 of (6+7sqrt(x)) ?

The integral from 0 to 4 of (6+7sqrt(x)) is 184/3

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integral from 0 to 4 of (6+7sqrt(x))

\int_{0}^{4} (6 + 7 x) d x

\frac{184}{3}

Decimal

61.33333 \dots

Solution steps

\int_{0}^{4} 6 + 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} 6 d x + \int_{0}^{4} 7 x d x

\int_{0}^{4} 6 d x = 24

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

= 24 + \frac{112}{3}

Simplify

24 + \frac{112}{3} : \frac{184}{3}

= \frac{184}{3}

What is the integral from 0 to 4 of (6+7sqrt(x)) ?
The integral from 0 to 4 of (6+7sqrt(x)) is 184/3