What is the integral from 0 to 8 of 3x^2-36x+105 ?

The integral from 0 to 8 of 3x^2-36x+105 is 200

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integral from 0 to 8 of 3x^2-36x+105

\int_{0}^{8} 3 x^{2} - 36 x + 105 d x

200

Solution steps

\int_{0}^{8} 3 x^{2} - 36 x + 105 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}^{8} 3 x^{2} d x - \int_{0}^{8} 36 x d x + \int_{0}^{8} 105 d x

\int_{0}^{8} 3 x^{2} d x = 512

\int_{0}^{8} 36 x d x = 1152

\int_{0}^{8} 105 d x = 840

= 512 - 1152 + 840

Simplify

= 200

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What is the integral from 0 to 8 of 3x^2-36x+105 ?
The integral from 0 to 8 of 3x^2-36x+105 is 200