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

The integral from-2 to 1 of (-x+2-x^2) is 9/2

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

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

\frac{9}{2}

Decimal

4.5

Solution steps

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

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

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

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

= - (- \frac{3}{2}) + 6 - 3

Simplify

- (- \frac{3}{2}) + 6 - 3 : \frac{9}{2}

= \frac{9}{2}

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What is the integral from-2 to 1 of (-x+2-x^2) ?
The integral from-2 to 1 of (-x+2-x^2) is 9/2