What is the integral from 0 to 2 of (y+2-y^2) ?

The integral from 0 to 2 of (y+2-y^2) is 10/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 2 of (y+2-y^2)

\int_{0}^{2} (y + 2 - y^{2}) d y

\frac{10}{3}

Decimal

3.33333 \dots

Solution steps

\int_{0}^{2} y + 2 - y^{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_{0}^{2} y d y + \int_{0}^{2} 2 d y - \int_{0}^{2} y^{2} d y

\int_{0}^{2} y d y = 2

\int_{0}^{2} 2 d y = 4

\int_{0}^{2} y^{2} d y = \frac{8}{3}

= 2 + 4 - \frac{8}{3}

Simplify

2 + 4 - \frac{8}{3} : \frac{10}{3}

= \frac{10}{3}

What is the integral from 0 to 2 of (y+2-y^2) ?
The integral from 0 to 2 of (y+2-y^2) is 10/3