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using integration find the area enclosed between the two circles x 2 + y 2 = 4 and (x – 2) 2 + y 2 = 4

using integration find the area enclosed between the two circles x2 + y2 = 4 and (x – 2)2 + y2 = 4

Grade:12

1 Answers

Shobhit Varshney IIT Roorkee
askIITians Faculty 33 Points
6 years ago
Hi,

If we find the point of intersection of the two circles, we get (1,^{\sqrt{3}}) and (1,-^{\sqrt{3}})

So, using the integration, we can find the area enclosed in the following way :

\int_{-\sqrt{3}}^{\sqrt{3}} (2 +\sqrt{4-y^{2}}) – (\sqrt{4-y^{2}}) dy

Solve this to get the area enclosed.

thanks.............

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