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 11/3

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

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

\frac{11}{3}

Decimal

3.66666 \dots

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 = \frac{7}{3}

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

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

= - \frac{7}{3} - (- 3) + 3

Simplify

- \frac{7}{3} - (- 3) + 3 : \frac{11}{3}

= \frac{11}{3}

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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 11/3