What is the integral from-8 to 8 of 1/2 (64-x^2) ?

The integral from-8 to 8 of 1/2 (64-x^2) is 1024/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-8 to 8 of 1/2 (64-x^2)

\int_{- 8}^{8} \frac{1}{2} (64 - x^{2}) d x

\frac{1024}{3}

Decimal

341.33333 \dots

Solution steps

\int_{- 8}^{8} \frac{1}{2} (64 - x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{- 8}^{8} 64 - 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

= \frac{1}{2} (\int_{- 8}^{8} 64 d x - \int_{- 8}^{8} x^{2} d x)

\int_{- 8}^{8} 64 d x = 1024

\int_{- 8}^{8} x^{2} d x = \frac{1024}{3}

= \frac{1}{2} (1024 - \frac{1024}{3})

Simplify

\frac{1}{2} (1024 - \frac{1024}{3}) : \frac{1024}{3}

= \frac{1024}{3}

What is the integral from-8 to 8 of 1/2 (64-x^2) ?
The integral from-8 to 8 of 1/2 (64-x^2) is 1024/3