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Popular >

integral from 0 to 3 of |3x-5|

Solution

\int_{0}^{3} ∣ 3 x - 5 ∣ d x

Solution

\frac{41}{6}

+1

Decimal Notation

6.83333 \dots

Solution steps

\int_{0}^{3} ∣ 3 x - 5 ∣ d x

Eliminate Absolutes

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

\int_{0}^{\frac{5}{3}} - 3 x + 5 d x = \frac{25}{6}

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

= \frac{25}{6} + \frac{8}{3}

Simplify

\frac{25}{6} + \frac{8}{3} : \frac{41}{6}

= \frac{41}{6}

Popular Examples

derivative of 1-(3x/(x^3+27))

\frac{d}{d x} (1 - \frac{3 x}{x ^{3} + 27})

integral of (2-sqrt(t))/(t^2)

\int \frac{2 - t}{t ^{2}} d t

limit as x approaches-infinity of ((x^2-5x))/(x-2)

x \to - \infty lim (\frac{( x ^{2} - 5 x )}{x - 2})

\frac{d y}{d x} = 1 - 2 x

integral of xarctan(2x)

\int x arctan (2 x) d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of |3x-5| ?
The integral from 0 to 3 of |3x-5| is 41/6