If you have a function f(x) and if you integrate over dx with in certain limit (say) x = a to b, then you will get the area confined by the curve f(x) from x = a to b.
So you must need to learn the mathematical form of f(x) for calculating the area.
When you have only a curve but you donot know the mathematical form, then there are many fitting procedures to discover the mathematical form of f(x). Many people use the help of MATLAB, MATHEMATICA etc or his/her own package. But I am not an expert, once I used the help using MATLAB.
If all of the crest and troughs are in the same plane say positive plane then, also can we utilise to find the area in the curve.
Thank you Abesh for your response. A plane is formed by two coordinates say x-y plane, y-z plane, x-z plane. Accordingly you can also form a complex plane using real and imaginary coordinate axes - no problem, it is mathematics - an abstract idea you can imagine.
I have no idea about positive or negative planes. Just like real and complex numbers, I know real-plane and complex-plane.
I am integrating a function, if the function is positive then area will positive; if the function is negative in the range of integration, then the result of integration (the sum of the function at different points) will be negative.
The crests and troughs - it depends on the form of the function you are integrating. So no problem if you define your curve (the function) properly.
An integration is nothing but summation of products of two quantities. In your case it is summation over [dx.f(x)]. The limits are always important otherwise integration has no physical meaning.
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