The Area as a Double Integral
Problem 1
Find the general formula as a double integral in
rectangular coordinates that allows to find the area between the lines
x = a, x = b and the curves y
= g(x), y = f(x).

Problem 2
Find the general formula as a double integral in rectangular
coordinates that allows to find the area between the lines y
= c, y = d and the curves x =
(y),
x =
(y).

Problem 3
Find the general formula as a double integral in polar
coordinates that allows to find the area between the lines
=
,
=
and the curves
r = g(
),
r = f(
).

Problem 4
Find the general formula as a double integral in polar
coordinates that allows to find the area between the circles r
= a, r = b and the curves
=
(r),
=
(r).

Problem 5
The following graphics determine a series of curves
in polar coordinates and their general designation. Using the general
formulas of problems 4 or 5, find the area limited by the given
curves.