JEE Mains · Maths · STD 12 - 8. Application and integration
Consider a region \(\mathrm{R}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathrm{R}^{2}: \mathrm{x}^{2} \leq \mathrm{y} \leq 2 \mathrm{x}\right\}\) If a line \(\mathrm{y}=\alpha\) divides the area of region \(\mathrm{R}\) into two equal parts, then which of the following is true?
- A \(\alpha^{3}-6 \alpha^{2}+16=0\)
- B \(3 \alpha^{2}-8 \alpha+8=0\)
- C \(\alpha^{3}-6 \alpha^{3 / 2}-16=0\)
- D \(3 \alpha^{2}-8 \alpha^{3 / 2}+8=0\)
Answer & Solution
Correct Answer
(D) \(3 \alpha^{2}-8 \alpha^{3 / 2}+8=0\)
Step-by-step Solution
Detailed explanation
\(\mathrm{y} \geq \mathrm{x}^{2} \Rightarrow\) upper region of \(\mathrm{y}=\mathrm{x}^{2}\) \(\mathrm{y} \leq 2 \mathrm{x} \Rightarrow\) lower region of \(\mathrm{y}=2 \mathrm{x}\) According to ques, area of \(\mathrm{OABC}=2\) area of \(\mathrm{OAC}\)…
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