What is the integral from 0 to 5 of (5-|x-5|) ?

The integral from 0 to 5 of (5-|x-5|) is 25/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 5 of (5-|x-5|)

\int_{0}^{5} (5 - ∣ x - 5 ∣) d x

\frac{25}{2}

Decimal

12.5

Solution steps

\int_{0}^{5} 5 - ∣ x - 5 ∣ d x

Eliminate Absolutes

= \int_{0}^{5} 5 - (- x + 5) d x

Simplify

= \int_{0}^{5} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{5}

= [\frac{x ^{2}}{2}]_{0}^{5}

Compute the boundaries:

\frac{25}{2}

= \frac{25}{2}

\int_{1}^{6} \frac{5}{x} d x

\int_{0}^{1} k x d x

\int_{0}^{x} x sin (x) d x

\int_{3}^{x} t^{2} + 1 d t

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

What is the integral from 0 to 5 of (5-|x-5|) ?
The integral from 0 to 5 of (5-|x-5|) is 25/2