What is the integral from 0 to 2 of (sqrt(2x)+x) ?

The integral from 0 to 2 of (sqrt(2x)+x) is 14/3

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integral from 0 to 2 of (sqrt(2x)+x)

\int_{0}^{2} (2 x + x) d x

\frac{14}{3}

Decimal

4.66666 \dots

Solution steps

\int_{0}^{2} 2 x + x d x

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= \int_{0}^{2} 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_{0}^{2} 2 x d x + \int_{0}^{2} x d x

\int_{0}^{2} 2 x d x = \frac{8}{3}

\int_{0}^{2} x d x = 2

= \frac{8}{3} + 2

Simplify

\frac{8}{3} + 2 : \frac{14}{3}

= \frac{14}{3}

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What is the integral from 0 to 2 of (sqrt(2x)+x) ?
The integral from 0 to 2 of (sqrt(2x)+x) is 14/3