What's the best way to calculate the area of a wavy graph?

Question

I'm not sure if wavy is the best word to describe the graph but the slope is inconsistent and I tried calculating the area by sections and adding them together but it didn't give me an accurate answer. Is there a better way? Thanks.

Answer 1

If you know the function of the "wavy" line, then you can use a higher mathematics called, integral calculus to give you an exact answer.

If you're too young to be learning calculus, then your method is the only other way. There are some variations on your method that give a little more accuracy, but you basically have it right. Try using smaller sections for more accuracy.

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Answer 2

Assume that your wavy curve is denoted by f(x) so that the wavy curve is produced by graphing f(x) vs x.
The best way to find the area under this curve is to integrate it in the region that you wish:
area under curve = INTEGRAL|x=x0-->x1|f(x)dx

Another way that does not require calculus is to go to QuickMath solutions; there you put in the interval and the points and it will spit out for you what you neeed. But it is always better to have an analytic solution.

Answer 3

To repeat what previous posters have mentioned, if you know the function of the curve, then take the integral of that function.

If you know the function, but don't know how to do integrals, then please post:

1) the equation of the curve,
2) the upper and lower limits on the x-axis

I (or some other folks on here) can calculate the answer from there.