JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region bounded by \(y-x=2\) and \(x^{2}=y\) is equal to :
- A \(\frac{4}{3}\)
- B \(\frac{9}{2}\)
- C \(\frac{16}{3}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{9}{2}\)
Step-by-step Solution
Detailed explanation
\(y-x=2, x^{2}=y\) Now, \(x^{2}=2+x\) \(\Rightarrow x^{2}-x-2=0\) \(\Rightarrow(x+1)(x-2)=0\) \(\text { Area }=\int_{-1}^{2}\left(2+x-x^{2}\right)\) \(=\left|2 x+\frac{x^{2}}{2}-\frac{x^{3}}{3}\right|_{-1}^{2}\)…
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