AP EAMCET · Maths · Area Under Curves
If the area of the circle \(x^2+y^2=2\) is divided into two parts by the parabola \(y=x^2\), then the area (in sq units) of the larger part is
- A \(\frac{3 \pi}{2}-\frac{1}{3}\)
- B \(6 \pi-\frac{4}{3}\)
- C \(\frac{4 \pi}{3}-\frac{2}{3}\)
- D \(4 \pi-\frac{1}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{3 \pi}{2}-\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
Given equation of curves \(x^2+y^2=2 \text { and } y=x^2\) For point of intersection, on solving the given curves, we get \(\begin{aligned} & y^2+y-2=0 \Rightarrow y^2+2 y-y-2=0 \\ \Rightarrow & y(y+2)-1(y+2) =0 \\ \Rightarrow & y =1 \qquad {[\because y > 0] } \end{aligned}\)…
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