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AP EAMCET · Maths · Area Under Curves

The area (in sq. units) of the region lying in the first quadrant and enclosed by the \(X\)-axis, the straight line \(x-\sqrt{3} y=0\) and the circle \(x^2+y^2=4\), is

  1. A \(\frac{\pi}{3}\)
  2. B \(\frac{2 \pi}{3}\)
  3. C \(\frac{\pi}{2 \sqrt{3}}\)
  4. D \(\frac{2 \pi}{3 \sqrt{2}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\pi}{3}\)

Step-by-step Solution

Detailed explanation

Equation of given circle \(\begin{aligned} & \Rightarrow x^2+y^2=2^2 \\ & \therefore \text { radius }=2\end{aligned}\) and line \(x-\sqrt{3} y=0\) \[ \begin{aligned} (\sqrt{3} y)^2+y^2 & =4 \\ \Rightarrow \quad & 4 y^2=4 \Rightarrow y^2=1 \Rightarrow y= \pm 1 \end{aligned} \] If…