Area of a Circle with Integration

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1. The equation of a circle is (x-p)2 + (y-q)2 = r2 . The circumference of a circle is 2πr. Write the area of a circle in terms of the circumference.

2. Look at Circle 1: Use an integral to write the formula for the area of a circle using the equation with center (0,0) in terms of x, y, and r.

3. Look at Circle 2: Use an integral to write the formula for the area of a circle using the equation with center (p,q) in terms of x, y, and r.

4. What would the formula be for the area of the region (x-p)2 + (y-q)2 = r2 ; x>0?

Elizabeth Phillips, 2 December 2013, Created with GeoGebra