What is the integral from 2 to 5 of (-2x^2+12x-17) ?

The integral from 2 to 5 of (-2x^2+12x-17) is -3

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integral from 2 to 5 of (-2x^2+12x-17)

\int_{2}^{5} (- 2 x^{2} + 12 x - 17) d x

- 3

Solution steps

\int_{2}^{5} - 2 x^{2} + 12 x - 17 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_{2}^{5} 2 x^{2} d x + \int_{2}^{5} 12 x d x - \int_{2}^{5} 17 d x

\int_{2}^{5} 2 x^{2} d x = 78

\int_{2}^{5} 12 x d x = 126

\int_{2}^{5} 17 d x = 51

= - 78 + 126 - 51

Simplify

= - 3

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What is the integral from 2 to 5 of (-2x^2+12x-17) ?
The integral from 2 to 5 of (-2x^2+12x-17) is -3