What is the integral from 0 to 12 of x^2-4x+10 ?

The integral from 0 to 12 of x^2-4x+10 is 408

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integral from 0 to 12 of x^2-4x+10

\int_{0}^{12} x^{2} - 4 x + 10 d x

408

Solution steps

\int_{0}^{12} x^{2} - 4 x + 10 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}^{12} x^{2} d x - \int_{0}^{12} 4 x d x + \int_{0}^{12} 10 d x

\int_{0}^{12} x^{2} d x = 576

\int_{0}^{12} 4 x d x = 288

\int_{0}^{12} 10 d x = 120

= 576 - 288 + 120

Simplify

= 408

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What is the integral from 0 to 12 of x^2-4x+10 ?
The integral from 0 to 12 of x^2-4x+10 is 408