Tính tích phân I=0 to 1 (|2x-1|-|x|)dx

$I = \int\limits_0^1 {\left( {\left| {2x - 1} \right| - \left| x \right|} \right)dx}$

$\Rightarrow I = \int\limits_0^{\frac{1}{2}} {\left( { - 2x + 1 - x} \right)dx} + \int\limits_{\frac{1}{2}}^1 {\left( {2x - 1 - x} \right)dx}$

$= \left. {\left( { - \frac{{3{x^2}}}{2} + x} \right)} \right|_0^{\frac{1}{2}} + \left. {\left( {\frac{{{x^2}}}{2} - x} \right)} \right|_{\frac{1}{2}}^1 = \frac{{ - 3}}{8} + \frac{1}{2} + \frac{1}{2} - 1 - \frac{1}{8} + \frac{1}{2} = 0$