What is the integral from-12 to 6 of (-2x+12) ?

The integral from-12 to 6 of (-2x+12) is 324

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integral from-12 to 6 of (-2x+12)

\int_{- 12}^{6} (- 2 x + 12) d x

324

Solution steps

\int_{- 12}^{6} - 2 x + 12 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_{- 12}^{6} 2 x d x + \int_{- 12}^{6} 12 d x

\int_{- 12}^{6} 2 x d x = - 108

\int_{- 12}^{6} 12 d x = 216

= - (- 108) + 216

Simplify

= 324

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What is the integral from-12 to 6 of (-2x+12) ?
The integral from-12 to 6 of (-2x+12) is 324