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+4/3-1/e

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

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

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

Decimal

3.68373 \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{4}{3}

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

\int \frac{x ^{2}}{x ^{2} + x ^{4}} d x

x^{2} y d x + x^{3} d y = 0

x \to - 2 lim (- 2 x^{3} - 3 x^{2} + 8)

y^{^{'''}} + 5 y^{^{''}} + 7 y^{^{'}} - 13 y = 0

a re a 2 x^{2} + 5 x + 6, (- 2, 0)

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+4/3-1/e