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

The integral from-1 to 1 of e^y-y^2-2 is e-14/3-1/e

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

e - \frac{14}{3} - \frac{1}{e}

Decimal

- 2.31626 \dots

Solution steps

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

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^{y} d y - \int_{- 1}^{1} y^{2} d y - \int_{- 1}^{1} 2 d y

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

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

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

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

Combine the fractions

- 4 - \frac{2}{3} : - \frac{14}{3}

= e - \frac{14}{3} - \frac{1}{e}

What is the integral from-1 to 1 of e^y-y^2-2 ?
The integral from-1 to 1 of e^y-y^2-2 is e-14/3-1/e