Question

COROANA! Sa se afle aria figurii marginite de graficele functiilor $f, g :R->R , f(x)=- x^{2} +5x-3 , g(x)= 4x-9$ .

Answer 1

aflam puntele de intersectie a graficelor
4x-9=-x^2+5x-3
x^2-x-6=0
x1=-2;x2=3
A=$\int\limits^3_2 {(- x^{2} +5x-3-4x-9)} \, dx= \int\limits^3_2 {(- x^{2} +x+6)} \, dx = \\ =(- \frac{ x^{3} }{3}+ \frac{ x^{2} }{2}+6x)=(-9+ \frac{9}{2}+18)-( \frac{8}{3}+2-12)=- \frac{35}{3}+ \frac{5}{2}+30= \\ = \frac{125}{6}$