find the area bounded by y=2x, y=(x/2) and?xy=2


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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

	$\forall x \in R 2 x ⩾ \frac{x}{2} A = \int (2 x - \frac{x}{2}) d x = 2 \frac{1}{2} x^{2} - \frac{1}{2} \times \frac{1}{2} x^{2}$ $A = x^{2} - \frac{1}{4} x^{2} = \frac{3}{4} x^{2} A = \frac{3}{4} x^{2}$ $y = 2 x \to y x = 2 x^{2} = 2 \to x = \pm 1$ $y = \frac{x}{2} \to y x = \frac{1}{2} x^{2} = 2 \to x^{2} = 4 \to x = \pm 2$ $t h e n x y = 2 s o l u t i o n s a r e i n c o m p a t i b l e s$
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