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

The integral from-1 to 1 of x^2+2x-3 is -16/3

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

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

- \frac{16}{3}

Decimal

- 5.33333 \dots

Solution steps

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

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

\int_{- 1}^{1} 2 x d x = 0

\int_{- 1}^{1} 3 d x = 6

= \frac{2}{3} + 0 - 6

Simplify

\frac{2}{3} + 0 - 6 : - \frac{16}{3}

= - \frac{16}{3}

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What is the integral from-1 to 1 of x^2+2x-3 ?
The integral from-1 to 1 of x^2+2x-3 is -16/3