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

The integral from-3 to 3 of (27/2-3/2 x^2) is 54

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

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

54

Solution steps

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

\int_{- 3}^{3} \frac{27}{2} d x = 81

\int_{- 3}^{3} \frac{3}{2} x^{2} d x = 27

= 81 - 27

Simplify

= 54

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What is the integral from-3 to 3 of (27/2-3/2 x^2) ?
The integral from-3 to 3 of (27/2-3/2 x^2) is 54