CUET · MATHS · PYQ PAPER 2023
The area enclosed by the curves \(x y=4, y=x, x=e^2\) and the \(x\)-axis, is :
- A \(4-\log _e 2\)
- B \(10-2 \log _e4\)
- C \(6-2 \log _e 4\)
- D \(10-\log _e 8\)
Answer & Solution
Correct Answer
(A) \(4-\log _e 2\)
Step-by-step Solution
Detailed explanation
Intersection of \(y=x\) and \(y=4/x\): \(x^2=4 \implies x=2\). Area \(A = \int_0^2 x \, dx + \int_2^{e^2} \frac{4}{x} \, dx\) \(A = \left[\frac{x^2}{2}\right]_0^2 + \left[4 \log_e x\right]_2^{e^2}\) \(A = \left(\frac{2^2}{2} - 0\right) + (4 \log_e e^2 - 4 \log_e 2)\)…
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