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in Definite Integrals by (28.7k points)
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Using integration find the area of the region bounded by the curve y = \(\sqrt{4-x^2}, x^2+y^2-4x=0\) and the x-axis.

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Best answer

First, let us find the intersection points of the curve,

Given Equations are x2 + y2 = 4 and x2 + y2 – 4x = 0.

From both of the equations,

4x = 4

x = 1

Putting this value in x2 + y2 = 4, we get,

1 + y2 = 4

y2 = 3

y = ±√3

Thus the curves intersect at A(1, √3) and B(1, - √3)

The area to be found is shaded in the figure above.

Area of Shaded region

Area of Shaded region \(=2\frac{\pi}{3}\) square units.

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