\(\int\limits_0^3 {\left| {2x - 3} \right|dx} = \int\limits_0^{\frac{3}{2}} {\left| {2x - 3} \right|dx} + \int\limits_{\frac{3}{2}}^3 {\left| {2x - 3} \right|dx} = \int\limits_0^{\frac{3}{2}} {\left( {3 - 2x} \right)dx} + \int\limits_{\frac{3}{2}}^3 {\left( {2x - 3} \right)dx} \)
\( = \left( {3x - {x^2}} \right)\left| \begin{array}{l}\frac{3}{2}\\0\end{array} \right. + \left( {{x^2} - 3x} \right)\left| \begin{array}{l}3\\\frac{3}{2}\end{array} \right. = \left[ {\left( {\frac{9}{2} - \frac{9}{4}} \right) - 0} \right] + \left[ {\left( {{3^2} - 3.3} \right) - \left( {\frac{9}{4} - \frac{9}{2}} \right)} \right] = \frac{9}{2}\)