computing area between 2 curves

I have two curves from the 2 vetctors as a result of simulation. I want to find the area between these 2 curves. The curves are intersecting many times.

any ideas are appreciated!!

Answer 1

[AC]

Hi,

From scratch, you could try something like:

1/2*(abs(C1(2:end)-C2(2:end))+abs(C1(1:end-1)-C2(1:end-1)))*diff(I)'

where C1 and C2 are your curves and I the x-axis.

This will give you an estimate of the integral of C1(t)-C2(t) dt for t in I.

Cheers,

AC

[AC]

Sorry that didn't print out right: the estimate of the integral of the absolute value of C1-C2.

[Vijay]

Thank you AC for hte brief explanation. In you formula, what do you mean by I which you used in diff(I)?

[Luffy]

 see doc diff
If X is a vector, then diff(X) returns a vector, one element shorter than X, of differences between adjacent elements.

[Vijay]

if X is a vector from 1:10 say X-axis. then diff(X) is a vector of '1' nine times. What is the use of multiplying it??

Answer 2

[Luffy]

 If u know the vectors then try using polyarea & subtract them

[Vijay]

Thanks for the answer.

I know the vectors. They are column vectors. I computed the polyarea with those 2 vectors... what did you mean by substraction?

[Luffy]

 I put too much thought into it,ws thinking about finding area covered by each curve with x axis and then subtracting them to get area between them.

 Happy to know polyarea helped you

[AC]

Hi,

Substracting the two areas is ok if the curves don't cross and you substract in the right order (that is: highest - lowest). Otherwise you will end up with a wrong result. For example, take sin(x) and cos(x) between 0 and 2: int cos(t)-sin(t) dt = -0.5 approx. int abs(cos(t)-sin(t)) dt= 1.33 approx.

It's the second one that you want. So you should compute the area of the difference in absolute value (see my response below). Cheers,

AC