CUET · MATHS · PYQ PAPER 2023
The area enclosed by the curve \(x=8 \cos t, y=4 \sin t\) between the lines \(x=0\) and \(x=4 \sqrt{3}\) is:
- A \(8 \sqrt{2}+\frac{32 \pi}{3}\) units
- B \(4 \sqrt{3}+\frac{16 \pi}{3}\) units
- C \(8 \sqrt{3}+\frac{32 \pi}{3}\) units
- D \(32 \pi\) units
Answer & Solution
Correct Answer
(C) \(8 \sqrt{3}+\frac{32 \pi}{3}\) units
Step-by-step Solution
Detailed explanation
\(x=8 \cos t \implies dx = -8 \sin t \, dt\) \(x=0 \implies t=\frac{\pi}{2}\) \(x=4 \sqrt{3} \implies \cos t = \frac{4 \sqrt{3}}{8} = \frac{\sqrt{3}}{2} \implies t=\frac{\pi}{6}\)…
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