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 Notation

4.66666 \dots

Solution steps

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

Apply radical rule:

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}

\int_{- 5}^{0} x^{2} + 5 x d x

\int_{0}^{\frac{1}{2}} \frac{arctan ( x )}{x} d x

\int_{- 3}^{0} x^{2} + 6 x + 9 d x

\int_{0}^{5} \frac{3 x + 2}{x ^{2} + 9} d x

\int_{3}^{4} f (5^{x}) 5^{x} d x

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