The area bounded by the curves y = | x - 1 | + | x - 2 | and y = 3 is equal to [2023]

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Solution

Q.
The area bounded by the curves $y =$ $| x - 1 |$ $+$ $| x - 2 |$ and $y = 3$ is equal to [2023]

1 6

2 3

3 5

4 4

Ans.
(4)

$Required area is shaded in the given figure, which is a trapezium.$

$∴$ $Area = \frac{1}{2} \times Sum of parallel sides \times Height$

$= \frac{1}{2} \times (A B + C D) \times A M = \frac{1}{2} (1 + 3) \times 2 = 4 sq. units$

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