What is the integral from 1 to 7 of t^2-2t-15 ?

The integral from 1 to 7 of t^2-2t-15 is -24

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integral from 1 to 7 of t^2-2t-15

\int_{1}^{7} t^{2} - 2 t - 15 d t

- 24

Solution steps

\int_{1}^{7} t^{2} - 2 t - 15 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} 15 d t

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

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

\int_{1}^{7} 15 d t = 90

= 114 - 48 - 90

Simplify

= - 24

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What is the integral from 1 to 7 of t^2-2t-15 ?
The integral from 1 to 7 of t^2-2t-15 is -24