What is the area between the curves x^2 + y^2 = 36 and x^2 - 2x + y^2 - 2y = 2

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The area between the curves x^2 + y^2 = 36 and x^2 - 2x + y^2 - 2y = 2 has to be determined.

x^2 + y^2 = 36 is the equation of a circle with center (0,0) and radius 6.

x^2 - 2x + y^2 - 2y = 2

=> x^2 - 2x + 1 + y^2 - 2y + 1 = 4

=> (x - 1)^2 + (y - 1)^2 = 2^2

This is the equation of a circle with center (1, 1) and radius 2.

The circle x^2 - 2x + y^2 - 2y = 2 lies entirely within the circle x^2 + y^2 = 36. The area between the two curves is `pi*6^2 - pi*2^2` = `pi*(36 - 4) = 32*pi`

The area between the curves x^2 + y^2 = 36 and x^2 - 2x + y^2 - 2y = 2 is `32*pi`

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