TS EAMCET · Maths · Area Under Curves
The area (in sq. units) of the region bounded by the circle \(x^2+y^2=64\), positive \(x\)-axis and the line \(y=\sqrt{3} x\) is
- A \(\frac{16 \pi}{3}\)
- B \(\frac{8 \pi}{3}\)
- C \(\frac{64 \pi}{3}\)
- D \(\frac{32 \pi}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{32 \pi}{3}\)
Step-by-step Solution
Detailed explanation
\(x^2+y^2=64 \Rightarrow y=\sqrt{3} x\) \(\begin{aligned} & y^2=3 x^2 \Rightarrow x= \pm 4 \\ & \therefore \quad y=\sqrt{48}\end{aligned}\) Area \(=\int_0^4 y d x+\int_4^8 y_2 d x\)…
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