What is the integral from 0 to 3 of (-2x^2+6x) ?

The integral from 0 to 3 of (-2x^2+6x) is 9

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integral from 0 to 3 of (-2x^2+6x)

\int_{0}^{3} (- 2 x^{2} + 6 x) d x

9

Solution steps

\int_{0}^{3} - 2 x^{2} + 6 x 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_{0}^{3} 2 x^{2} d x + \int_{0}^{3} 6 x d x

\int_{0}^{3} 2 x^{2} d x = 18

\int_{0}^{3} 6 x d x = 27

= - 18 + 27

Simplify

= 9

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What is the integral from 0 to 3 of (-2x^2+6x) ?
The integral from 0 to 3 of (-2x^2+6x) is 9