What is the integral from 1 to 7 of (t^2-4t-12) ?

The integral from 1 to 7 of (t^2-4t-12) is -54

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integral from 1 to 7 of (t^2-4t-12)

\int_{1}^{7} (t^{2} - 4 t - 12) d t

- 54

Solution steps

\int_{1}^{7} t^{2} - 4 t - 12 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} 4 t d t - \int_{1}^{7} 12 d t

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

\int_{1}^{7} 4 t d t = 96

\int_{1}^{7} 12 d t = 72

= 114 - 96 - 72

Simplify

= - 54

What is the integral from 1 to 7 of (t^2-4t-12) ?
The integral from 1 to 7 of (t^2-4t-12) is -54