JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region \(R = \{(x, y): xy \leq 27, 1 \leq y \leq x^2\}\) is equal to:
- A \(78\log_e 3 - \dfrac{52}{3}\)
- B \(54\log_e 3 - \dfrac{52}{3}\)
- C \(54\log_e 3 - \dfrac{26}{3}\)
- D \(54\log_e 3 + \dfrac{26}{3}\)
Answer & Solution
Correct Answer
(B) \(54\log_e 3 - \dfrac{52}{3}\)
Step-by-step Solution
Detailed explanation
The given region is bounded by the curves \(y = 1\), \(y = x^2\), and \(xy = 27\) in the first quadrant. Let us find the points of intersection of these curves: Intersection of \(y = 1\) and \(y = x^2\) gives \(x = 1\). Intersection of \(y = x^2\) and \(xy = 27\) gives…
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