Question

Use a graphing utility to graph the polar equations and find the area of the given region.

Common interior of r = 4 sin θ and r = 2

Answer 1

Step 1:

The equation of curves are and .

Find the point of intersection of the two curves.

General solution of is .

If then .

If then .

Point of intersections are and .

Step 2:

Graph:

Draw the polar plane.

Plot the curves and .

Plot the intersection points.

Observe the Graph:

From to , the region is bounded by the curve and it is shown as blue in color.

From to , the region is bounded by the curve and it is shown as pale yellow in color.

From to , the region is bounded by the curve and it is shown as blue in color.

Step 3:

Area of the region bounded by the curve is .

Area of the region bounded by the curves is

 Area of the region bounded by the curves is

Solution:

Area of the region bounded by the curves is