What is the integral from 2 to 5 of (x^2-2x+3) ?

The integral from 2 to 5 of (x^2-2x+3) is 27

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integral from 2 to 5 of (x^2-2x+3)

\int_{2}^{5} (x^{2} - 2 x + 3) d x

27

Solution steps

\int_{2}^{5} x^{2} - 2 x + 3 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_{2}^{5} x^{2} d x - \int_{2}^{5} 2 x d x + \int_{2}^{5} 3 d x

\int_{2}^{5} x^{2} d x = 39

\int_{2}^{5} 2 x d x = 21

\int_{2}^{5} 3 d x = 9

= 39 - 21 + 9

Simplify

= 27

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What is the integral from 2 to 5 of (x^2-2x+3) ?
The integral from 2 to 5 of (x^2-2x+3) is 27