JEE Mains · Maths · STD 12 - 8. Application and integration
The area (in \(sq. units\)) of the region \(A = \left\{ {\left( {x,y} \right):\frac{{{y^2}}}{2} \le x \le y + 4} \right\}\) is
- A \(\frac{{53}}{3}\)
- B \(18\)
- C \(30\)
- D \(16\)
Answer & Solution
Correct Answer
(B) \(18\)
Step-by-step Solution
Detailed explanation
\(y^{2}=2 x\) ...\((1)\) and \(x-y-4=0\) ....\((2)\) solving \(( 1)\) and \(( 2)\) \((x-y)^{2}=2 x\) \(\Rightarrow x^{2}-10 x+16=0\) \(\Rightarrow x=8,2\) and \(y=4,-2\) \(A = \int\limits_{ - 2}^4 {\left( {y + 4 - \frac{{{y^2}}}{2}} \right)dy} \)…
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