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

The integral from 0 to 2 of sqrt(x+2)-x is (16-4sqrt(2))/3-2

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

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

\frac{16 - 4 2}{3} - 2

Decimal

1.44771 \dots

Solution steps

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

\int_{0}^{2} x + 2 d x = \frac{16 - 4 2}{3}

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

= \frac{16 - 4 2}{3} - 2

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What is the integral from 0 to 2 of sqrt(x+2)-x ?
The integral from 0 to 2 of sqrt(x+2)-x is (16-4sqrt(2))/3-2