- #1
kahwawashay1
- 96
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What is ∫sin(sin(x)) dx ?
I was told that it was not an elementary function. Then what function is it?
I was told that it was not an elementary function. Then what function is it?
kahwawashay1 said:What is ∫sin(sin(x)) dx ?
I was told that it was not an elementary function. Then what function is it?
Dick said:I don't think it has a name yet. Do you want to name it?
Solve what?kahwawashay1 said:Haha how can it not be already named? Can't someone solve it?
kahwawashay1 said:Haha how can it not be already named? Can't someone solve it?
Dick said:Some integrals that can't be expressed as elementary functions are useful enough that they are given special names. E.g. http://en.wikipedia.org/wiki/Exponential_integral Not being able to 'solve' something doesn't it isn't useful or that there is nothing you can say about it.
kahwawashay1 said:ohhh
But I just downloaded Mathematica, and when I integrate sin(sin(x)), it gives me: (1/2)(sin2(x2))
But I can't see how taking the derivative of that gives sinsinx
Is Mathematica wrong then?
Integrating ∫sin(sin(x)) dx means finding the function whose derivative is sin(sin(x)). In other words, we are looking for a function whose slope at any given point is equal to sin(sin(x)).
Integrating functions allows us to find the total change or area under a curve. This is useful in many fields of science, such as physics, engineering, and economics.
Yes, it is possible to solve this integral analytically by using integration techniques such as substitution or integration by parts. However, the resulting integral may be complex and difficult to evaluate.
The steps to solve this integral may vary depending on the integration technique used. Generally, the steps involve using a substitution to simplify the integral, integrating the resulting function, and then substituting back the original variable.
This integral has various applications in science and engineering, such as in the analysis of waveforms, fluid mechanics, and signal processing. It is also used in solving differential equations and in calculating the work done by a force over a given distance.