What is the integral from-3 to 3 of (27-3x^2) ?

The integral from-3 to 3 of (27-3x^2) is 108

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integral from-3 to 3 of (27-3x^2)

\int_{- 3}^{3} (27 - 3 x^{2}) d x

108

Solution steps

\int_{- 3}^{3} 27 - 3 x^{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_{- 3}^{3} 27 d x - \int_{- 3}^{3} 3 x^{2} d x

\int_{- 3}^{3} 27 d x = 162

\int_{- 3}^{3} 3 x^{2} d x = 54

= 162 - 54

Simplify

= 108

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What is the integral from-3 to 3 of (27-3x^2) ?
The integral from-3 to 3 of (27-3x^2) is 108