What is the integral from-2 to 1 of (x^2-2x+3) ?

The integral from-2 to 1 of (x^2-2x+3) is 15

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integral from-2 to 1 of (x^2-2x+3)

\int_{- 2}^{1} (x^{2} - 2 x + 3) d x

15

Solution steps

\int_{- 2}^{1} 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}^{1} x^{2} d x - \int_{- 2}^{1} 2 x d x + \int_{- 2}^{1} 3 d x

\int_{- 2}^{1} x^{2} d x = 3

\int_{- 2}^{1} 2 x d x = - 3

\int_{- 2}^{1} 3 d x = 9

= 3 - (- 3) + 9

Simplify

= 15

What is the integral from-2 to 1 of (x^2-2x+3) ?
The integral from-2 to 1 of (x^2-2x+3) is 15