Is it possible to find areas between three or more curves

[madah12]

I looked in my james stewart book and didn't find any thing helpful about that and google didn't give me any useful results so is it possible and how to?

 

[chiro]

I looked in my james stewart book and didn't find any thing helpful about that and google didn't give me any useful results so is it possible and how to?

The Riemann mapping theorem states that if a region is simple, then there exists a valid transformation to a rectangle.

What might be easier is to to look at the different areas and decompose them in the same way that you would decompose functions if you had a discontinuous function and wanted to integrate.

Take the following example:

f(x) = (x + 1)^2 if x < 0, 2 if 0 <= x <= 1, and x^3 if x > 1

If you were to find the integral you would break it up into three parts and integrate each part.

Do basically the same thing which would look something like this:

1) Find the intersection points of your areas
2) With each intersection find the appropriate expressions that bound the area for that section
3) Do a piecewise integration to get the bounded area

Hope that helps!

 

[wil3]

I'm nor sure exactly what you mean. Do you mean a region bounded by more than two curves? This is possible, but it often requires breaking the region up into several integrals. This is because a "slice" of the function parallel to the y-axis will only pass through two of the functions (assuming that we are dealing with standard 1:1 functions here). So the integral is the difference between the two functions in 2 dimensions.

This may be a swing and a miss reply, however, so please add some more information if this answer is non-responsive to the situations you are talking about.

Best of luck!