What is the integral from 0 to 12 of 2000-12t^2 ?

The integral from 0 to 12 of 2000-12t^2 is 17088

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integral from 0 to 12 of 2000-12t^2

\int_{0}^{12} 2000 - 12 t^{2} d t

17088

Solution steps

\int_{0}^{12} 2000 - 12 t^{2} 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_{0}^{12} 2000 d t - \int_{0}^{12} 12 t^{2} d t

\int_{0}^{12} 2000 d t = 24000

\int_{0}^{12} 12 t^{2} d t = 6912

= 24000 - 6912

Simplify

= 17088

What is the integral from 0 to 12 of 2000-12t^2 ?
The integral from 0 to 12 of 2000-12t^2 is 17088