What is the integral from 0 to 4 of sqrt(x+2)-x ?

The integral from 0 to 4 of sqrt(x+2)-x is 4sqrt(6)-(4sqrt(2))/3-8

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integral from 0 to 4 of sqrt(x+2)-x

\int_{0}^{4} x + 2 - x d x

46 - \frac{4 2}{3} - 8

Decimal

- 0.08765 \dots

Solution steps

\int_{0}^{4} x + 2 - 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} x + 2 d x - \int_{0}^{4} x d x

\int_{0}^{4} x + 2 d x = 46 - \frac{4 2}{3}

\int_{0}^{4} x d x = 8

= 46 - \frac{4 2}{3} - 8

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What is the integral from 0 to 4 of sqrt(x+2)-x ?
The integral from 0 to 4 of sqrt(x+2)-x is 4sqrt(6)-(4sqrt(2))/3-8