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

The integral from-1 to 1 of e^x-x^2-1 is e-8/3-1/e

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

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

e - \frac{8}{3} - \frac{1}{e}

Decimal

- 0.31626 \dots

Solution steps

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

\int_{- 1}^{1} e^{x} d x = e - \frac{1}{e}

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

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

= e - \frac{1}{e} - \frac{2}{3} - 2

Combine the fractions

- 2 - \frac{2}{3} : - \frac{8}{3}

= e - \frac{8}{3} - \frac{1}{e}

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