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

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