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

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

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

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

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

Solution steps

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

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

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

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

= \frac{2}{3} - 4 - (e - \frac{1}{e})

Simplify

\frac{2}{3} - 4 - (e - \frac{1}{e}) : - e + \frac{1}{e} - \frac{10}{3}

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

\int_{0}^{π} sin (t) d t

y^{^{'}} = 2 x - y

\frac{d}{d x} (3^{x^{2} - x + 5})

\frac{d}{d x} (\frac{x ^{2} + 10 x}{( x + 5 ) ^{2}})

\frac{\partial}{\partial x} (4 u (x, y))

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