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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

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

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

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

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

Simplify

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

= \frac{9}{2}

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\int_{0}^{2 - x} 2 - x - y d y

\int_{0}^{2} 4 x (x^{2} + 1)^{3} d x

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