What is the integral from-3 to 3 of [(18-x^2)-(x^2)] ?

The integral from-3 to 3 of [(18-x^2)-(x^2)] is 72

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-3 to 3 of [(18-x^2)-(x^2)]

\int_{- 3}^{3} [(18 - x^{2}) - (x^{2})] d x

72

Solution steps

\int_{- 3}^{3} 18 - x^{2} - x^{2} d x

Simplify

= \int_{- 3}^{3} 18 - 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_{- 3}^{3} 18 d x - \int_{- 3}^{3} 2 x^{2} d x

\int_{- 3}^{3} 18 d x = 108

\int_{- 3}^{3} 2 x^{2} d x = 36

= 108 - 36

Simplify

= 72

What is the integral from-3 to 3 of [(18-x^2)-(x^2)] ?
The integral from-3 to 3 of [(18-x^2)-(x^2)] is 72