What is the integral from-3 to 3 of (12-x^2-(x^2-6)) ?

The integral from-3 to 3 of (12-x^2-(x^2-6)) is 72

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-3 to 3 of (12-x^2-(x^2-6))

\int_{- 3}^{3} (12 - x^{2} - (x^{2} - 6)) d x

72

Solution steps

\int_{- 3}^{3} 12 - x^{2} - (x^{2} - 6) d x

Simplify

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

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

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

= - 36 + 108

Simplify

= 72

\int_{0}^{1} 2 e^{\frac{x}{3} + 4} d x

\int_{1}^{\infty} 6 x^{- 7} d x

\int_{1}^{4} f (x + 5) d x

\int_{0}^{1} 10 x^{4} e^{x^{5}} d x

\int_{1}^{e^{3}} \frac{1}{x} d x

What is the integral from-3 to 3 of (12-x^2-(x^2-6)) ?
The integral from-3 to 3 of (12-x^2-(x^2-6)) is 72