What is the integral from 0 to 3 of 3x^2-24x+45 ?

The integral from 0 to 3 of 3x^2-24x+45 is 54

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integral from 0 to 3 of 3x^2-24x+45

\int_{0}^{3} 3 x^{2} - 24 x + 45 d x

54

Solution steps

\int_{0}^{3} 3 x^{2} - 24 x + 45 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} 24 x d x + \int_{0}^{3} 45 d x

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

\int_{0}^{3} 24 x d x = 108

\int_{0}^{3} 45 d x = 135

= 27 - 108 + 135

Simplify

= 54

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What is the integral from 0 to 3 of 3x^2-24x+45 ?
The integral from 0 to 3 of 3x^2-24x+45 is 54