Area of the region bounded by y=|x| and y=-|x | vedclass

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Question

(C) The region is bounded by the curves $y=|x|$ and $y=-|x|+2$.To find the intersection points,set $|x| = -|x| + 2$,which gives $2|x| = 2$,so $|x| = 1

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$2 	ext{ sq units}$

Vedclass · Answer

(C) The region is bounded by the curves $y=|x|$ and $y=-|x|+2$.To find the intersection points,set $|x| = -|x| + 2$,which gives $2|x| = 2$,so $|x| = 1$,implying $x = 1$ or $x = -1$.For $x=1$,$y=1$. For $x=-1$,$y=1$.The vertices of the bounded region are $(0,0)$,$(1,1)$,$(0,2)$,and $(-1,1)$.This region is a square with vertices $O(0,0)$,$C(1,1)$,$B(0,2)$,and $A(-1,1)$.The length of the side of the square is the distance between $(0,0)$ and $(1,1)$,which is $\sqrt{(1-0)^2 + (1-0)^2} = \sqrt{1+1} = \sqrt{2}$.The area of the square is $(	ext{side})^2 = (\sqrt{2})^2 = 2 	ext{ sq units}$.

Area of the region bounded by $y=|x|$ and $y=-|x|+2$ is

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