COMEDK · Maths · 31. Area Under Curves
The area of the region in the first quadrant enclosed by the \(x\)-axis, the line \(x = \sqrt{3}\,y\) and the circle \(x^2 + y^2 = 4\) is
- A \(\dfrac{\pi}{6}\ sq\ units\)
- B \(\dfrac{\pi}{3}\ sq\ units\)
- C \(\pi\ sq\ units\)
- D \(\dfrac{2\pi}{3}\ sq\ units\)
Answer & Solution
Correct Answer
(B) \(\dfrac{\pi}{3}\ sq\ units\)
Step-by-step Solution
Detailed explanation
The given circle is \(x^2 + y^2 = 4\), which has its center at the origin \((0,0)\) and radius \(r = 2\). The given line is \(x = \sqrt{3}y\), which can be rewritten as \(y = \dfrac{1}{\sqrt{3}}x\). The angle made by this line with the positive \(x\)-axis is…
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