What is the integral from-2 to 4 of (x+4-(x^2)/2) ?

The integral from-2 to 4 of (x+4-(x^2)/2) is 18

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integral from-2 to 4 of (x+4-(x^2)/2)

\int_{- 2}^{4} (x + 4 - \frac{x ^{2}}{2}) d x

18

Solution steps

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

\int_{- 2}^{4} x d x = 6

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

\int_{- 2}^{4} \frac{x ^{2}}{2} d x = 12

= 6 + 24 - 12

Simplify

= 18

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What is the integral from-2 to 4 of (x+4-(x^2)/2) ?
The integral from-2 to 4 of (x+4-(x^2)/2) is 18