What is the integral from-3 to 3 of (x+2)(x-2) ?

The integral from-3 to 3 of (x+2)(x-2) is -6

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integral from-3 to 3 of (x+2)(x-2)

\int_{- 3}^{3} (x + 2) (x - 2) d x

- 6

Solution steps

\int_{- 3}^{3} (x + 2) (x - 2) d x

Expand

(x + 2) (x - 2) : x^{2} - 4

= \int_{- 3}^{3} x^{2} - 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_{- 3}^{3} x^{2} d x - \int_{- 3}^{3} 4 d x

\int_{- 3}^{3} x^{2} d x = 18

\int_{- 3}^{3} 4 d x = 24

= 18 - 24

Simplify

= - 6

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What is the integral from-3 to 3 of (x+2)(x-2) ?
The integral from-3 to 3 of (x+2)(x-2) is -6