JEE Main 2022 Mathematics question

The area of the bounded region enclosed by the curve y = 3 − |x − 1/2| − |x + 1| and the x-axis is

(1)9/4
(2)45/16
(3)27/8Correct
(4)63/16

Answer: (3)

Solution

For x < −1, y = 3 − (1/2 − x) + (x + 1) = 2x + 7/2. For −1 , y = 3 − (1/2 − x) − (x + 1) = 3/2. For x > 1/2, y = 3 − (x − 1/2) − (x + 1) = 5/2 − 2x. The curve meets the x-axis

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Question ID VK-034874