The document discusses methods for calculating the area of planar regions bounded by curves in rectangular and polar coordinate systems using definite integrals. For regions bounded by curves in the rectangular system, formulas are provided for calculating the area when the curves have different signs or one curve is above the other. In polar coordinates, the area of a sector bounded by curves is calculated using a definite integral involving the radius function. Examples are worked out applying these methods to find the areas of specific geometric regions.
The document discusses methods for calculating the area of planar regions bounded by curves in rectangular and polar coordinate systems using definite integrals. For regions bounded by curves in the rectangular system, formulas are provided for calculating the area when the curves have different signs or one curve is above the other. In polar coordinates, the area of a sector bounded by curves is calculated using a definite integral involving the radius function. Examples are worked out applying these methods to find the areas of specific geometric regions.