Write down a procedure describing
your method for calculating the line integral
without resort to iterated integrals).
How can iterated integrals be
used to evaluate line integrals? What opportunities does this relationship
between line integrals and iterated integrals present?
Suppose you had
a region of the plane that resembled the region D shown below.
How could you establish
whether or not the relationship between line integrals and iterated integrals
worked for such a region?
Explain how the relationship between
line integrals and iterated integrals can be used to calculate areas of the
plane using line integrals.
Suppose you were given a planimeter
that had no information about how to convert the readings from the planimeter
into areas. How would you go about establishing the relationship between the
readings from the planimeter and the corresponding areas?