Q. 7

# Calculate the area of the region between the circles x^{2} + y^{2} = 4 and (x – 2)^{2} + y^{2} = 4.

Answer :

Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by .

Given; x^{2} + y^{2} = 4 and (x – 2)^{2} + y^{2} = 4

By solving; x^{2} + 4 − (x – 2)^{2} = 4

⇒ x^{2} − x^{2} + 4x − 4 = 0

∴ x = 1 is the point of intersection.

Required Area

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