What is the integral from-8 to 4 of x/2-sqrt(8-x) ?

The integral from-8 to 4 of x/2-sqrt(8-x) is -148/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-8 to 4 of x/2-sqrt(8-x)

\int_{- 8}^{4} \frac{x}{2} - 8 - x d x

- \frac{148}{3}

Decimal

- 49.33333 \dots

Solution steps

\int_{- 8}^{4} \frac{x}{2} - 8 - x 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_{- 8}^{4} \frac{x}{2} d x - \int_{- 8}^{4} 8 - x d x

\int_{- 8}^{4} \frac{x}{2} d x = - 12

\int_{- 8}^{4} 8 - x d x = \frac{112}{3}

= - 12 - \frac{112}{3}

Simplify

- 12 - \frac{112}{3} : - \frac{148}{3}

= - \frac{148}{3}

\int_{1}^{2} 10 - 5 x d x

\int_{0}^{4} (5 x - x^{2} - x) d x

\int_{0}^{π} (6 e^{x} + 5 sin (x)) d x

\int_{0}^{5} (x^{2} - 6) d x

\int_{0}^{3} \frac{5}{x + 4} d x

What is the integral from-8 to 4 of x/2-sqrt(8-x) ?
The integral from-8 to 4 of x/2-sqrt(8-x) is -148/3