en

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 |3x-8|

Solution

\int_{0}^{5} ∣ 3 x - 8 ∣ d x

Solution

\frac{113}{6}

+1

Decimal Notation

18.83333 \dots

Solution steps

\int_{0}^{5} ∣ 3 x - 8 ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{8}{3}} - 3 x + 8 d x + \int_{\frac{8}{3}}^{5} 3 x - 8 d x

\int_{0}^{\frac{8}{3}} - 3 x + 8 d x = \frac{32}{3}

\int_{\frac{8}{3}}^{5} 3 x - 8 d x = \frac{49}{6}

= \frac{32}{3} + \frac{49}{6}

Simplify

\frac{32}{3} + \frac{49}{6} : \frac{113}{6}

= \frac{113}{6}

Popular Examples

integral from-1 to 3 of (2x-x^2)

\int_{- 1}^{3} (2 x - x^{2}) d x

integral from 1 to 2 of xe^{-x^2+1}

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

integral from 0 to pi/2 of (sin(2t))

\int_{0}^{\frac{π}{2}} (sin (2 t)) d t

integral from 0 to 1 of sqrt(4x+3)

\int_{0}^{1} 4 x + 3 d x

integral from 2 to 4 of x/((x^2+1)^3)

\int_{2}^{4} \frac{x}{( x ^{2} + 1 ) ^{3}} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 5 of |3x-8| ?
The integral from 0 to 5 of |3x-8| is 113/6