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

The integral from-2 to 2 of (2sqrt(4-x^2))^2 is 128/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{128}{3}

Decimal

42.66666 \dots

Solution steps

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

Apply Integration By Parts

= [4 x (4 - x^{2}) - \int - 8 x^{2} d x]_{- 2}^{2}

\int - 8 x^{2} d x = - \frac{8 x ^{3}}{3}

= [4 x (4 - x^{2}) - (- \frac{8 x ^{3}}{3})]_{- 2}^{2}

Simplify

= [4 x (4 - x^{2}) + \frac{8 x ^{3}}{3}]_{- 2}^{2}

Compute the boundaries:

\frac{128}{3}

= \frac{128}{3}

What is the integral from-2 to 2 of (2sqrt(4-x^2))^2 ?
The integral from-2 to 2 of (2sqrt(4-x^2))^2 is 128/3