CUET · MATHS · PYQ PAPER 2023
Area bounded by \(y=|x-5|\) and the \(x\)-axis between \(x=2\) and \(x=4\) is:
- A 5
- B 4
- C 3
- D 6
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
\(y=|x-5|\) for \(x \in [2,4]\) is \(y=5-x\). Area \(=\int_{2}^{4} (5-x) \, dx\) \(= [5x - \frac{x^2}{2}]_{2}^{4}\) \(= (5(4) - \frac{4^2}{2}) - (5(2) - \frac{2^2}{2})\) \(= (20 - 8) - (10 - 2)\) \(= 12 - 8\) \(= 4\)
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