CUET · MATHS · PYQ PAPER 2023
The area (in sq. units) enclosed by the curve \(y=\frac{1}{2} x|x|\) and the line \(y=x\) is :
- A 1
- B \(\frac{4}{3}\)
- C \(\frac{5}{3}\)
- D 2
Answer & Solution
Correct Answer
(B) \(\frac{4}{3}\)
Step-by-step Solution
Detailed explanation
The curve is \(y=\begin{cases} \frac{1}{2}x^2 & \text{if } x \ge 0 \\ -\frac{1}{2}x^2 & \text{if } x Intersection points: \( \frac{1}{2}x|x|=x \implies x|x|-2x=0 \implies x(|x|-2)=0 \). \(x=0\) or \(|x|=2 \implies x=\pm 2\). Intersection points are \((-2,-2)\),…
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