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

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

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

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

- 78

Solution steps

\int_{1}^{7} t^{2} - 2 t - 24 d t

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} t^{2} d t - \int_{1}^{7} 2 t d t - \int_{1}^{7} 24 d t

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

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

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

= 114 - 48 - 144

Simplify

= - 78

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