Reference no: EM131584166

Question: 1) Consider the region enclosed by the curve r = 4cosθ and the rays θ = 6Π and θ = 4Π - a.

a) Sketch the region.

b) Calculate the area of the region analytically.

c) Compute the perimeter of the region.

2) Consider the cardiod r = 1 - cosθ.

a) Analytically determine the total enclosed area of the cardiod.

b) Compute the perimeter of the cardiod .

c) Find the area bounded by the cardiod and the y-axis in the first quadrant.

d) Find the area bounded by the caridiod, the polar axis and the y-axis in the third quadrant.

3) Let A be the region in the interior of r = 4 cos θ and in the exterior of r = 1. Calculate both the area and the perimeter of region A.

4) Find both the area and the perimeter of the region enclosed by r = 0.5 and one petal of the rose curve r = cos 3θ.

5) Compute the area of the region between the inner and outer loop of the limacon r = 2 cos θ - 1.