What is the integral from 0 to 3 of 3x^2-12x+9 ?

The integral from 0 to 3 of 3x^2-12x+9 is 0

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integral from 0 to 3 of 3x^2-12x+9

\int_{0}^{3} 3 x^{2} - 12 x + 9 d x

0

Solution steps

\int_{0}^{3} 3 x^{2} - 12 x + 9 d x

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}^{3} 3 x^{2} d x - \int_{0}^{3} 12 x d x + \int_{0}^{3} 9 d x

\int_{0}^{3} 3 x^{2} d x = 27

\int_{0}^{3} 12 x d x = 54

\int_{0}^{3} 9 d x = 27

= 27 - 54 + 27

Simplify

= 0

What is the integral from 0 to 3 of 3x^2-12x+9 ?
The integral from 0 to 3 of 3x^2-12x+9 is 0