Oblicz pole obszaru ograniczonego krzywymi  [latex]y = x^{2} - x + 1 oraz y = 2x - 1[/latex]

[latex]egin{cases}y=x^2-x+1\y=2x-1end{cases}\ \ x^2-x+1=2x-1\ x^2-3x+2=0\ (x-1)(x-2)=0\ x=1 vee x=2\ \ \ intlimits^2_1 {(x^2-3x+2)} dx =(frac{1}{3}x^3-frac{3}{2}x^2+2x|^{2}_{1}=(frac{1}{3}cdot 2^3-frac{3}{2}cdot 2^2+2cdot 2)-\ \-(frac{1}{3}cdot 1^3-frac{3}{2}cdot 1^2+2cdot 1)=(frac{8}{3}-6+4)-(frac{1}{3}-frac{2}{3}+2)=\ \=frac{2}{3}-frac{5}{3}=|-1|=1[/latex]