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

The integral from-2 to 0 of (x^2-2x+3) is 38/3

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

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

\frac{38}{3}

Decimal

12.66666 \dots

Solution steps

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

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

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

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

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

Simplify

\frac{8}{3} - (- 4) + 6 : \frac{38}{3}

= \frac{38}{3}

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What is the integral from-2 to 0 of (x^2-2x+3) ?
The integral from-2 to 0 of (x^2-2x+3) is 38/3