AP EAMCET · Maths · Area Under Curves
The area of the region lying between the curves \(y=\sqrt{4-x^2}, y^2=3 x\) and the Y-axis is
- A \(\frac{\pi}{3}-\frac{1}{2 \sqrt{3}}\)
- B \(\frac{\pi}{6}+\frac{1}{2 \sqrt{3}}\)
- C \(\frac{\pi}{3}+\frac{1}{2 \sqrt{3}}\)
- D \(\frac{\pi}{6}-\frac{1}{2 \sqrt{3}}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{3}-\frac{1}{2 \sqrt{3}}\)
Step-by-step Solution
Detailed explanation
\(y=\sqrt{4-x^2} \implies x^2+y^2=4\) \(y^2=3x\) Intersection: \(x^2+3x=4 \implies x^2+3x-4=0 \implies (x+4)(x-1)=0\) \(x=1\) (since in 1st quadrant, \(x \ge 0\)) Area \(A = \int_0^1 (\sqrt{4-x^2} - \sqrt{3x}) dx\)…
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