What is the integral from-6 to 0 of ([ 1/2 x]+|x|) ?

The integral from-6 to 0 of ([ 1/2 x]+|x|) is 9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-6 to 0 of ([ 1/2 x]+|x|)

\int_{- 6}^{0} ([\frac{1}{2} x] + ∣ x ∣) d x

9

Solution steps

\int_{- 6}^{0} [\frac{1}{2} x] + ∣ x ∣ d x

Eliminate Absolutes

= \int_{- 6}^{0} [\frac{1}{2} x] - 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_{- 6}^{0} \frac{1}{2} x d x - \int_{- 6}^{0} x d x

\int_{- 6}^{0} \frac{1}{2} x d x = - 9

\int_{- 6}^{0} x d x = - 18

= - 9 - (- 18)

Simplify

= 9

\int_{- 1}^{3} ∣ x ∣ - 1 d x

\int_{0}^{5} \frac{1}{25 - t ^{2}} d t

\int_{1}^{3} \frac{1}{x ^{4}} d x

\int_{0}^{1} 5 x + 6 d x

\int_{1}^{4} 2 x^{2} d x

What is the integral from-6 to 0 of ([ 1/2 x]+|x|) ?
The integral from-6 to 0 of ([ 1/2 x]+|x|) is 9