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

The integral from-2 to 4 of (2x+4)-(x^2-4) is 36

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

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

36

Solution steps

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

Simplify

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

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

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

\int_{- 2}^{4} 8 d x = 48

= - 24 + 12 + 48

Simplify

= 36

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What is the integral from-2 to 4 of (2x+4)-(x^2-4) ?
The integral from-2 to 4 of (2x+4)-(x^2-4) is 36