정적분 등식

$\displaystyle \int _{0} ^{a} \left( 4 x ^{2} - 3 x \right) dx = \int _{0} ^{a} \left( x ^{2} + x \right) dx$에서 $\displaystyle \int _{0} ^{a} \left( 4 x ^{2} - 3 x \right) dx - \int _{0} ^{a} \left( x ^{2} + x \right) dx$ $\displaystyle = \int _{0} ^{a} \left( 3 x ^{2} - 4 x \right) dx$ $\displaystyle = \left[ \begin{array}{l} \begin{matrix} \\ \end{matrix} x ^{3} - 2 x ^{2} \end{array} \right] _{0} ^{a}$ $= a ^{3} - 2 a ^{2} = a ^{2} \left( a - 2 \right) = 0$ 따라서 $a > 0$이므로 $a = 2$