What is the integral from 1 to 0 of (x^2-2x+2) ?

The integral from 1 to 0 of (x^2-2x+2) is -4/3

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integral from 1 to 0 of (x^2-2x+2)

\int_{1}^{0} (x^{2} - 2 x + 2) d x

- \frac{4}{3}

Solution steps

\int_{1}^{0} x^{2} - 2 x + 2 d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} 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_{0}^{1} x^{2} d x - \int_{0}^{1} 2 x d x + \int_{0}^{1} 2 d x)

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\int_{0}^{1} 2 x d x = 1

\int_{0}^{1} 2 d x = 2

= - (\frac{1}{3} - 1 + 2)

Simplify

- (\frac{1}{3} - 1 + 2) : - \frac{4}{3}

= - \frac{4}{3}

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What is the integral from 1 to 0 of (x^2-2x+2) ?
The integral from 1 to 0 of (x^2-2x+2) is -4/3