The area of the region bounded by curves y=|x-2|, x=1,x=3 and x-axis is

Question

A.   6

B.   2

C.  1

D.  4

Answer 1

Answer is C.

Here’s why. y=|x-2| is a V-shaped “curve” which forms two triangles created by limits for x.

Plot the points A(1,1), B(2,0) and C(3,1). The area you need is the area of the right triangle with hypotenuse AB, plus the area of the right triangle with hypotenuse BC. These triangles are congruent and are each half a unit square in area, like dividing a unit square into two halves by drawing a diagonal. So the area is the area of a unit square which is 1.