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.

 


 
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