What is the integral from-2 to 2 of (sqrt(4-x^2))^2 ?

The integral from-2 to 2 of (sqrt(4-x^2))^2 is 32/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-2 to 2 of (sqrt(4-x^2))^2

\int_{- 2}^{2} (4 - x^{2})^{2} d x

\frac{32}{3}

Solution steps

\int_{- 2}^{2} (4 - x^{2})^{2} d x

Simplify

(4 - x^{2})^{2} : 4 - x^{2}

= \int_{- 2}^{2} 4 - 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_{- 2}^{2} 4 d x - \int_{- 2}^{2} x^{2} d x

\int_{- 2}^{2} 4 d x = 16

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

= 16 - \frac{16}{3}

Simplify

16 - \frac{16}{3} : \frac{32}{3}

= \frac{32}{3}

\frac{d}{d x} ((5 x - 3)^{4} (2 x - 7)^{- 3})

(\frac{1}{2 x})^{^{'}}

θ cos (θ)

\int (2 x - 4^{x}) d x

y = x^{2} - 4, y = 5

What is the integral from-2 to 2 of (sqrt(4-x^2))^2 ?
The integral from-2 to 2 of (sqrt(4-x^2))^2 is 32/3