What is the integral from 0 to 5 of 3t^2-36t+105 ?

The integral from 0 to 5 of 3t^2-36t+105 is 200

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integral from 0 to 5 of 3t^2-36t+105

\int_{0}^{5} 3 t^{2} - 36 t + 105 d t

200

Solution steps

\int_{0}^{5} 3 t^{2} - 36 t + 105 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}^{5} 3 t^{2} d t - \int_{0}^{5} 36 t d t + \int_{0}^{5} 105 d t

\int_{0}^{5} 3 t^{2} d t = 125

\int_{0}^{5} 36 t d t = 450

\int_{0}^{5} 105 d t = 525

= 125 - 450 + 525

Simplify

= 200

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What is the integral from 0 to 5 of 3t^2-36t+105 ?
The integral from 0 to 5 of 3t^2-36t+105 is 200