What is the integral from 0 to 2 of |(x-1)(3x-1)| ?

The integral from 0 to 2 of |(x-1)(3x-1)| is 62/27

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integral from 0 to 2 of |(x-1)(3x-1)|

\int_{0}^{2} ∣ (x - 1) (3 x - 1) ∣ d x

\frac{62}{27}

Decimal

2.29629 \dots

Solution steps

\int_{0}^{2} ∣ (x - 1) (3 x - 1) ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{1}{3}} (x - 1) (3 x - 1) d x + \int_{\frac{1}{3}}^{1} - 3 x^{2} + 4 x - 1 d x + \int_{1}^{2} (x - 1) (3 x - 1) d x

\int_{0}^{\frac{1}{3}} (x - 1) (3 x - 1) d x = \frac{4}{27}

\int_{\frac{1}{3}}^{1} - 3 x^{2} + 4 x - 1 d x = \frac{4}{27}

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

= \frac{4}{27} + \frac{4}{27} + 2

Simplify

\frac{4}{27} + \frac{4}{27} + 2 : \frac{62}{27}

= \frac{62}{27}

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What is the integral from 0 to 2 of |(x-1)(3x-1)| ?
The integral from 0 to 2 of |(x-1)(3x-1)| is 62/27