JEE Mains · Maths · STD 12 - 8. Application and integration
The area (in sq. units) of the region described by \(A = \{ (x,y)|y \ge {x^2} - 5x + 4,\,x + y \ge 1,\,y \le 0\} \) is
- A \(\frac {19}{6}\)
- B \(\frac {17}{6}\)
- C \(\frac {7}{2}\)
- D \(\frac {13}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac {19}{6}\)
Step-by-step Solution
Detailed explanation
Required area \(=A_{1}+A_{2}\) \(=\frac{1}{2} \times 2 \times 2+\left|\int_{3}^{4}\left(x^{2}-5 x+4\right) d x\right|\) \(=2+\frac{7}{6}=\frac{19}{6}\) sq units
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