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

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

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integral from 0 to 2 of (-x^2+3x-2)

\int_{0}^{2} (- x^{2} + 3 x - 2) d x

- \frac{2}{3}

Decimal

- 0.66666 \dots

Solution steps

\int_{0}^{2} - x^{2} + 3 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}^{2} x^{2} d x + \int_{0}^{2} 3 x d x - \int_{0}^{2} 2 d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 3 x d x = 6

\int_{0}^{2} 2 d x = 4

= - \frac{8}{3} + 6 - 4

Simplify

- \frac{8}{3} + 6 - 4 : - \frac{2}{3}

= - \frac{2}{3}

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