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

The integral from-3 to 1 of (x^2+x-2) is -8/3

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

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

- \frac{8}{3}

Decimal Notation

- 2.66666 \dots

Solution steps

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

\int_{- 3}^{1} x^{2} d x = \frac{28}{3}

\int_{- 3}^{1} x d x = - 4

\int_{- 3}^{1} 2 d x = 8

= \frac{28}{3} - 4 - 8

Simplify

\frac{28}{3} - 4 - 8 : - \frac{8}{3}

= - \frac{8}{3}

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\int_{2}^{10} \frac{1}{5 x - 1} d x

What is the integral from-3 to 1 of (x^2+x-2) ?
The integral from-3 to 1 of (x^2+x-2) is -8/3