What is the integral from 1 to 7 of (x^2-2x-24) ?

The integral from 1 to 7 of (x^2-2x-24) is -78

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integral from 1 to 7 of (x^2-2x-24)

\int_{1}^{7} (x^{2} - 2 x - 24) d x

- 78

Solution steps

\int_{1}^{7} x^{2} - 2 x - 24 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_{1}^{7} x^{2} d x - \int_{1}^{7} 2 x d x - \int_{1}^{7} 24 d x

\int_{1}^{7} x^{2} d x = 114

\int_{1}^{7} 2 x d x = 48

\int_{1}^{7} 24 d x = 144

= 114 - 48 - 144

Simplify

= - 78

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What is the integral from 1 to 7 of (x^2-2x-24) ?
The integral from 1 to 7 of (x^2-2x-24) is -78