What is the integral from-3 to-1 of (-6x^2+3x+7) ?

The integral from-3 to-1 of (-6x^2+3x+7) is -50

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integral from-3 to-1 of (-6x^2+3x+7)

\int_{- 3}^{- 1} (- 6 x^{2} + 3 x + 7) d x

- 50

Solution steps

\int_{- 3}^{- 1} - 6 x^{2} + 3 x + 7 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}^{- 1} 6 x^{2} d x + \int_{- 3}^{- 1} 3 x d x + \int_{- 3}^{- 1} 7 d x

\int_{- 3}^{- 1} 6 x^{2} d x = 52

\int_{- 3}^{- 1} 3 x d x = - 12

\int_{- 3}^{- 1} 7 d x = 14

= - 52 - 12 + 14

Simplify

= - 50

\int_{0}^{1} 2 x + 2 d x

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What is the integral from-3 to-1 of (-6x^2+3x+7) ?
The integral from-3 to-1 of (-6x^2+3x+7) is -50