   Chapter 7.P, Problem 4P

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# The centers of two disks with radius 1 are one unit apart. Find the area of the union of the two disks.

To determine

To find:

The area of the union of the two disks.

Explanation

Given:

x2+y2=1 and (x1)2+y2=1

Formulae used:

The integration method.

Consider x2+y2=1 and (x1)2+y2=1

The following diagram depicts the area to be computed.

Divide the enclosed region into thin horizontal strips of width dy and length

x2x1=1y2+1y21

Therefore, the required area is

A=2032</

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