(inner loop).
Solution:
To determine the boundaries of the inner loop note:
The curve starts at (1,0)
continues on to (3,Pi/2)
continues on to (1,Pi)
reaches the origin for the first time at 7Pi/6
reaches the highest point of the inner loop at 3Pi/2
returns to the origin at 11Pi/6
and then returns to the starting point (1,2Pi)
Therefore, the entire inner loop starts at 7Pi/6 and ends at 11Pi/6.
By use of symmetry, we can evaluate the function from
and multiply by 2 to get the area of the entire loop.
by:sh