What is the integral from 0 to 8 of 6t^2-2t+5 ?

The integral from 0 to 8 of 6t^2-2t+5 is 1000

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integral from 0 to 8 of 6t^2-2t+5

\int_{0}^{8} 6 t^{2} - 2 t + 5 d t

1000

Solution steps

\int_{0}^{8} 6 t^{2} - 2 t + 5 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}^{8} 6 t^{2} d t - \int_{0}^{8} 2 t d t + \int_{0}^{8} 5 d t

\int_{0}^{8} 6 t^{2} d t = 1024

\int_{0}^{8} 2 t d t = 64

\int_{0}^{8} 5 d t = 40

= 1024 - 64 + 40

Simplify

= 1000

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What is the integral from 0 to 8 of 6t^2-2t+5 ?
The integral from 0 to 8 of 6t^2-2t+5 is 1000