What is the integral from-3 to 3 of (9x-4x^2) ?

The integral from-3 to 3 of (9x-4x^2) is -72

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integral from-3 to 3 of (9x-4x^2)

\int_{- 3}^{3} (9 x - 4 x^{2}) d x

- 72

Solution steps

\int_{- 3}^{3} 9 x - 4 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} 9 x d x - \int_{- 3}^{3} 4 x^{2} d x

\int_{- 3}^{3} 9 x d x = 0

\int_{- 3}^{3} 4 x^{2} d x = 72

= 0 - 72

Simplify

= - 72

What is the integral from-3 to 3 of (9x-4x^2) ?
The integral from-3 to 3 of (9x-4x^2) is -72