The area of the region bounded by the curve y = max {|x|, x|x – 2|}, the x-axis and the lines x = –2 and x = 4 is equal to _________. [2025]

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Solution

Q.
The area of the region bounded by the curve y = max ${| x |, x | x - 2 |}$ , the x-axis and the lines x = –2 and x = 4 is equal to _________. [2025]

Ans.
(12)

Required Area = Area of $△$ OAB + Area of region OCDEO

$= \frac{1}{2} \times 2 \times 2 + \int_{0}^{1} (2 x - x^{2}) d x + \int_{1}^{3} x d x + \int_{3}^{4} (x^{2} - 2 x) d x$

$= 2 + \frac{2}{3} + 4 + \frac{16}{3}$

= 12 sq. units.

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