Menu Close

find-the-area-abounded-y-x-afind-y-x-2-




Question Number 67106 by mhmd last updated on 22/Aug/19
find the area abounded y=(√x)  afind y=x−2?
$${find}\:{the}\:{area}\:{abounded}\:{y}=\sqrt{{x}} \\ $$$${afind}\:{y}={x}−\mathrm{2}? \\ $$
Commented by kaivan.ahmadi last updated on 24/Aug/19
x−2=(√x)⇒x^2 −5x+4=0⇒(x−1)(x−4)=0⇒   { ((x=1)),((x=2)) :}  ∫((√x)−x+2)dx=((2x(√x))/3)−(x^2 /2)+2x∣_1 ^2 =  ((4/3)(√2)−2+4)−((2/3)−(1/2)+2)=(4/3)(√2)−(1/6)
$${x}−\mathrm{2}=\sqrt{{x}}\Rightarrow{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{4}=\mathrm{0}\Rightarrow\left({x}−\mathrm{1}\right)\left({x}−\mathrm{4}\right)=\mathrm{0}\Rightarrow \\ $$$$\begin{cases}{{x}=\mathrm{1}}\\{{x}=\mathrm{2}}\end{cases} \\ $$$$\int\left(\sqrt{{x}}−{x}+\mathrm{2}\right){dx}=\frac{\mathrm{2}{x}\sqrt{{x}}}{\mathrm{3}}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{2}{x}\mid_{\mathrm{1}} ^{\mathrm{2}} = \\ $$$$\left(\frac{\mathrm{4}}{\mathrm{3}}\sqrt{\mathrm{2}}−\mathrm{2}+\mathrm{4}\right)−\left(\frac{\mathrm{2}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{2}\right)=\frac{\mathrm{4}}{\mathrm{3}}\sqrt{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{6}} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *