What is the integral from 0 to 3 of (6x-x^2)-x^2 ?

The integral from 0 to 3 of (6x-x^2)-x^2 is 9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 3 of (6x-x^2)-x^2

\int_{0}^{3} (6 x - x^{2}) - x^{2} d x

9

Solution steps

\int_{0}^{3} 6 x - x^{2} - x^{2} d x

Simplify

= \int_{0}^{3} 6 x - 2 x^{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_{0}^{3} 6 x d x - \int_{0}^{3} 2 x^{2} d x

\int_{0}^{3} 6 x d x = 27

\int_{0}^{3} 2 x^{2} d x = 18

= 27 - 18

Simplify

= 9

What is the integral from 0 to 3 of (6x-x^2)-x^2 ?
The integral from 0 to 3 of (6x-x^2)-x^2 is 9