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

The integral from-1 to 2 of (x^2-2x+2) is 6

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

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

6

Solution steps

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

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

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

\int_{- 1}^{2} 2 d x = 6

= 3 - 3 + 6

Simplify

= 6

What is the integral from-1 to 2 of (x^2-2x+2) ?
The integral from-1 to 2 of (x^2-2x+2) is 6