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Popular Calculus >

integral from 0 to 1 of |2x-1|

Solution

\int_{0}^{1} ∣ 2 x - 1 ∣ d x

Solution

\frac{1}{2}

+1

Decimal

0.5

Solution steps

\int_{0}^{1} ∣ 2 x - 1 ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{1}{2}} - 2 x + 1 d x + \int_{\frac{1}{2}}^{1} 2 x - 1 d x

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

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

= \frac{1}{4} + \frac{1}{4}

Simplify

\frac{1}{4} + \frac{1}{4} : \frac{1}{2}

= \frac{1}{2}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of |2x-1| ?
The integral from 0 to 1 of |2x-1| is 1/2