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

The integral from-1 to 1 of (-x^2-x+2) is 10/3

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

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

\frac{10}{3}

Decimal

3.33333 \dots

Solution steps

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

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

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

\int_{- 1}^{1} 2 d x = 4

= - \frac{2}{3} - 0 + 4

Simplify

- \frac{2}{3} - 0 + 4 : \frac{10}{3}

= \frac{10}{3}

What is the integral from-1 to 1 of (-x^2-x+2) ?
The integral from-1 to 1 of (-x^2-x+2) is 10/3