Question

the area of the region bounded by the curves \[y=|x-1|~~and~~y=3-|x|~~is~~??\]

Answer 1

have you tried drawing the curves ?

Answer 2

yeah having problems with that , the mod expression is problematic :v

Answer 3

actually \[f(x)=|x|\\~~~~~~~=x~~when~~x>0\\~~~~~~~=-x ~~~when ~~x<0\]
try to use this .
so the given equations will be like\[y=|x-1|\\~~~~=x-1,~~when ~~x>1\\~~~~=-(x-1)=-x+1, when~~ x \le 1\\AND\\ y=3-|x|\\~~~~=3-x, when ~~x>0\\~~~~~=3+x,when ~~x \le 0\]
getting my point ?
now try to draw the lines

Answer 4

the shaded portion is your area required
now just use basic geometry and its done !!