What is the integral from 1 to 4 of (2x+sqrt(x)) ?

The integral from 1 to 4 of (2x+sqrt(x)) is 59/3

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integral from 1 to 4 of (2x+sqrt(x))

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

\frac{59}{3}

Decimal

19.66666 \dots

Solution steps

\int_{1}^{4} 2 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}^{4} 2 x d x + \int_{1}^{4} x d x

\int_{1}^{4} 2 x d x = 15

\int_{1}^{4} x d x = \frac{14}{3}

= 15 + \frac{14}{3}

Simplify

15 + \frac{14}{3} : \frac{59}{3}

= \frac{59}{3}

What is the integral from 1 to 4 of (2x+sqrt(x)) ?
The integral from 1 to 4 of (2x+sqrt(x)) is 59/3