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

The integral from-1 to 1 of (e^x-(x^2-2)) is e+10/3-1/e

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

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

e + \frac{10}{3} - \frac{1}{e}

Decimal

5.68373 \dots

Solution steps

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

Simplify

= \int_{- 1}^{1} e^{x} - x^{2} + 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}^{1} e^{x} d x - \int_{- 1}^{1} x^{2} d x + \int_{- 1}^{1} 2 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} 2 d x = 4

= e - \frac{1}{e} - \frac{2}{3} + 4

Combine the fractions

4 - \frac{2}{3} : \frac{10}{3}

= e + \frac{10}{3} - \frac{1}{e}

What is the integral from-1 to 1 of (e^x-(x^2-2)) ?
The integral from-1 to 1 of (e^x-(x^2-2)) is e+10/3-1/e