What is the integral from-3 to 3 of (2+sqrt(9-x^2)) ?

The integral from-3 to 3 of (2+sqrt(9-x^2)) is 12+(9pi)/2

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 (2+sqrt(9-x^2))

\int_{- 3}^{3} (2 + 9 - x^{2}) d x

12 + \frac{9 π}{2}

Decimal

26.13716 \dots

Solution steps

\int_{- 3}^{3} 2 + 9 - 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} 2 d x + \int_{- 3}^{3} 9 - x^{2} d x

\int_{- 3}^{3} 2 d x = 12

\int_{- 3}^{3} 9 - x^{2} d x = \frac{9 π}{2}

= 12 + \frac{9 π}{2}

What is the integral from-3 to 3 of (2+sqrt(9-x^2)) ?
The integral from-3 to 3 of (2+sqrt(9-x^2)) is 12+(9pi)/2