What is the integral from-3 to 3 of (12-x^2)-(x^2-6) ?

The integral from-3 to 3 of (12-x^2)-(x^2-6) is 72

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integral from-3 to 3 of (12-x^2)-(x^2-6)

\int_{- 3}^{3} (12 - x^{2}) - (x^{2} - 6) d x

72

Solution steps

\int_{- 3}^{3} 12 - x^{2} - (x^{2} - 6) d x

Simplify

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

\int_{- 3}^{3} 2 x^{2} d x = 36

\int_{- 3}^{3} 18 d x = 108

= - 36 + 108

Simplify

= 72

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What is the integral from-3 to 3 of (12-x^2)-(x^2-6) ?
The integral from-3 to 3 of (12-x^2)-(x^2-6) is 72