JEE Mains · Maths · STD 12 - 8. Application and integration
The area (in sq. units) of the region \(A\,\, = \,\left\{ {\left( {x\,,\,y} \right)\,:\,{x^2}\, \le \,y\, \le \,x + 2} \right\}\) is
- A \(\frac {31}{6}\)
- B \(\frac {13}{6}\)
- C \(\frac {9}{2}\)
- D \(\frac {10}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac {9}{2}\)
Step-by-step Solution
Detailed explanation
\(x^{2} \leq y \leq x+2\) \(x^{2}=y ; y=x+2\) \(x^{2}=x+2\) \(x^{2}-x-2=0\) \((x-2)(x-1)=0\) \(x=2,-1\) Area \( = \int\limits_{ - 1}^2 {(x + 2) - } {x^2}dx = \frac{9}{2}\)
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