Answer
\begin{align}
\int_0^1 |2x-1| \ dx = \frac{1}{2}
\end{align}
Work Step by Step
$\text{The given definite integral is}$
\begin{align}
\int_0^1 |2x-1| \ dx
\end{align}
$\text{The alternative way to calculate the integral is to find the area under}$
$\text{the function. The given modulus function forms 2 right triangles. The}$
$\text{area of each triangle is:}$
\begin{align}
A = \frac{1}{2} \times 1 \times \frac{1}{2} = \frac{1}{4}
\end{align}
$\text{Thus, the total area and consequently, the value of the definite integral:}$
\begin{align}
\int_0^1 |2x-1| \ dx = 2 \times A = \frac{1}{2}
\end{align}
