What is the integral from 2 to 8 of sqrt(2x)-x+4 ?

The integral from 2 to 8 of sqrt(2x)-x+4 is 38/3

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integral from 2 to 8 of sqrt(2x)-x+4

\int_{2}^{8} 2 x - x + 4 d x

\frac{38}{3}

Decimal

12.66666 \dots

Solution steps

\int_{2}^{8} 2 x - x + 4 d x

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= \int_{2}^{8} 2 x - x + 4 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_{2}^{8} 2 x d x - \int_{2}^{8} x d x + \int_{2}^{8} 4 d x

\int_{2}^{8} 2 x d x = \frac{56}{3}

\int_{2}^{8} x d x = 30

\int_{2}^{8} 4 d x = 24

= \frac{56}{3} - 30 + 24

Simplify

\frac{56}{3} - 30 + 24 : \frac{38}{3}

= \frac{38}{3}

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What is the integral from 2 to 8 of sqrt(2x)-x+4 ?
The integral from 2 to 8 of sqrt(2x)-x+4 is 38/3