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Question: The area of the region bounded by y=\|x-1\| and y = 1 is...

The area of the region bounded by y=|x-1| and y = 1 is

A

1

B

2

C

1/2

D

None of these

Answer

1

Explanation

Solution

Required Area

= ∫01(x2−x1)dy=∫01{(x+1)−(−x+1)}dx\int_{0}^{1}{\left( x_{2} - x_{1} \right)dy = \int_{0}^{1}{\left\{ (x + 1) - ( - x + 1) \right\} dx}}

= ∫012xdx=[x2]01=1\int_{0}^{1}{2xdx = \left\lbrack x^{2} \right\rbrack_{0}^{1} = 1}