Question Number 66731 by aditya730222@gmail.com last updated on 19/Aug/19
$${y}={x}^{\mathrm{2}} −\mathrm{3}{x}\:\:\:\:\:{y}=\mathrm{2}{x}\:{find}\:{area} \\ $$
Commented by Tony Lin last updated on 19/Aug/19
![x^2 −3x=2x x(x−5)=0 ∫_0 ^5 [2x−(x^2 −3x)]dx =∫_0 ^5 (−x^2 +5x)dx =[−(1/3)x^3 +(5/2)x^2 ]_0 ^5 =((125)/6)](Q66735.png)
$${x}^{\mathrm{2}} −\mathrm{3}{x}=\mathrm{2}{x} \\ $$$${x}\left({x}−\mathrm{5}\right)=\mathrm{0} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{5}} \left[\mathrm{2}{x}−\left({x}^{\mathrm{2}} −\mathrm{3}{x}\right)\right]{dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{5}} \left(−{x}^{\mathrm{2}} +\mathrm{5}{x}\right){dx} \\ $$$$=\left[−\frac{\mathrm{1}}{\mathrm{3}}{x}^{\mathrm{3}} +\frac{\mathrm{5}}{\mathrm{2}}{x}^{\mathrm{2}} \right]_{\mathrm{0}} ^{\mathrm{5}} \\ $$$$=\frac{\mathrm{125}}{\mathrm{6}} \\ $$