JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region \(S=\left\{(x, y): y^{2} \leq 8 x, y \geq \sqrt{2} x, x \geq 1\right\}\) is
- A \(\frac{13 \sqrt{2}}{6}\)
- B \(\frac{11 \sqrt{2}}{6}\)
- C \(\frac{5 \sqrt{2}}{6}\)
- D \(\frac{19 \sqrt{2}}{6}\)
Answer & Solution
Correct Answer
(B) \(\frac{11 \sqrt{2}}{6}\)
Step-by-step Solution
Detailed explanation
\(y^{2}=8 x.......(1)\) \(y=\sqrt{2} x.........(2)\) \(y^{2}=2 x^{2}\) \(\Rightarrow 8 x=2 x^{2}\) \(\Rightarrow x=0 \,\,and \,\,4\) Area \(:=\int\limits_{1}^{4}\, 2 \sqrt{2} \sqrt{x}-\sqrt{2} x \,d x\)…
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