Question
The area of the region bounded by the curves $$y = \left| {x - 2} \right|,\,x = 1,\,x = 3$$ and the x-axis is-
A.
$$4$$
B.
$$2$$
C.
$$3$$
D.
$$1$$
Answer :
$$1$$
Solution :
The required area is shown by shaded region
$$\eqalign{ & A = \int\limits_1^3 {\left| {x - 2} \right|dx} \,\,\, = 2\int\limits_2^3 {\left( {x - 2} \right)dx} \cr & = 2\left[ {\frac{{{x^2}}}{2} - 2x} \right]_2^3\,\,\, = 1 \cr} $$
The required area is shown by shaded region
$$\eqalign{ & A = \int\limits_1^3 {\left| {x - 2} \right|dx} \,\,\, = 2\int\limits_2^3 {\left( {x - 2} \right)dx} \cr & = 2\left[ {\frac{{{x^2}}}{2} - 2x} \right]_2^3\,\,\, = 1 \cr} $$