JEE Mains · Maths · STD 12 - 8. Application and integration
The area (in sq. units) of the region \(A=\{(x, y)\) \(\left.:|x|+|y| \leq 1,2 y^{2} \geq|x|\right\}\) is
- A \(\frac{1}{6}\)
- B \(\frac{1}{3}\)
- C \(\frac{7}{6}\)
- D \(\frac{5}{6}\)
Answer & Solution
Correct Answer
(D) \(\frac{5}{6}\)
Step-by-step Solution
Detailed explanation
\(|x|+|y| \leq 1\) \(2 y^{2} \geq|x|\) For point of intersection \(x+y=1 \Rightarrow x=1-y\) \(y^{2}=\frac{x}{2} \Rightarrow 2 y^{2}=x\) \(2 y^{2}=1-y \Rightarrow 2 y^{2}+y-1=0\) \((2 y-1)(y+1)=0\) \(y=\frac{1}{2}\) or -1 Now Area of…
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