find-the-area-bounded-by-y-2x-y-x-2-and-xy-2-

Question Number 145774 by Engr_Jidda last updated on 08/Jul/21

f i n d t h e a r e a b o u n d e d b y y = 2 x, y = \frac{x}{2} a n d ? x y = 2

Answered by ArielVyny last updated on 08/Jul/21

\forall x \in R 2 x ⩾ \frac{x}{2} A = \int (2 x - \frac{x}{2}) d x = 2 \frac{1}{2} x^{2} - \frac{1}{2} \times \frac{1}{2} x^{2}

A = x^{2} - \frac{1}{4} x^{2} = \frac{3}{4} x^{2} A = \frac{3}{4} x^{2}

y = 2 x \to y x = 2 x^{2} = 2 \to x = \pm 1

y = \frac{x}{2} \to y x = \frac{1}{2} x^{2} = 2 \to x^{2} = 4 \to x = \pm 2

t h e n x y = 2 s o l u t i o n s a r e i n c o m p a t i b l e s