What is the integral from 1 to 3 of 3t^2-12t+9 ?

The integral from 1 to 3 of 3t^2-12t+9 is -4

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integral from 1 to 3 of 3t^2-12t+9

\int_{1}^{3} 3 t^{2} - 12 t + 9 d t

- 4

Solution steps

\int_{1}^{3} 3 t^{2} - 12 t + 9 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}^{3} 3 t^{2} d t - \int_{1}^{3} 12 t d t + \int_{1}^{3} 9 d t

\int_{1}^{3} 3 t^{2} d t = 26

\int_{1}^{3} 12 t d t = 48

\int_{1}^{3} 9 d t = 18

= 26 - 48 + 18

Simplify

= - 4

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What is the integral from 1 to 3 of 3t^2-12t+9 ?
The integral from 1 to 3 of 3t^2-12t+9 is -4