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

The integral from 1 to-1 of x^2-1 is 4/3

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integral from 1 to-1 of x^2-1

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

\frac{4}{3}

Solution steps

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

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

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

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

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

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

Simplify

- (\frac{2}{3} - 2) : \frac{4}{3}

= \frac{4}{3}

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What is the integral from 1 to-1 of x^2-1 ?
The integral from 1 to-1 of x^2-1 is 4/3