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Popular Calculus >

integral from 0 to 3 of |3x-1|

Solution

\int_{0}^{3} ∣ 3 x - 1 ∣ d x

Solution

\frac{65}{6}

+1

Decimal

10.83333 \dots

Solution steps

\int_{0}^{3} ∣ 3 x - 1 ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{1}{3}} - 3 x + 1 d x + \int_{\frac{1}{3}}^{3} 3 x - 1 d x

\int_{0}^{\frac{1}{3}} - 3 x + 1 d x = \frac{1}{6}

\int_{\frac{1}{3}}^{3} 3 x - 1 d x = \frac{32}{3}

= \frac{1}{6} + \frac{32}{3}

Simplify

\frac{1}{6} + \frac{32}{3} : \frac{65}{6}

= \frac{65}{6}

Graph

Popular Examples

(\partial)/(\partial x)(x^2+xy+3y)

\frac{\partial}{\partial x} (x^{2} + x y + 3 y)

integral of (z+1)e^{2z}

\int (z + 1) e^{2 z} d z

integral of x(x^2-3)^3

\int x (x^{2} - 3)^{3} d x

(\partial)/(\partial x)(a^{-x})

\frac{\partial}{\partial x} (a^{- x})

derivative of x/(\sqrt[3]{x^2+4})

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of |3x-1| ?
The integral from 0 to 3 of |3x-1| is 65/6