Dear All,

I'm trying to find a primitive of f(x)=cos(-Asin(x)) where A is a constant number.

I've tried Wolfram but unsuccessfully. An approximate function of this primitive would also be welcome.

Thanks for your help !

Kind Regards.

Started by baltoche, Jan 20, 2017

5 replies to this topic

Posted 20 January 2017 - 12:44 PM

Dear All,

I'm trying to find a primitive of f(x)=cos(-Asin(x)) where A is a constant number.

I've tried Wolfram but unsuccessfully. An approximate function of this primitive would also be welcome.

Thanks for your help !

Kind Regards.

Posted 20 January 2017 - 12:58 PM

Would a numerical integration method not do nicely?

Posted 20 January 2017 - 01:35 PM

Wolfram did not work because the primitive of this function is not an "elementary function" (so cannot be written in terms of trig functions, exponentals, logs, etc.).

Posted 23 January 2017 - 07:51 PM

I know the values between whom I need to integrate this function, but it does not solve my issue... Regarding numerical methods (calculating a rough surface for instance), I cannot do it since my final integral will be a function of A.

If the answer is not an elementary function, is there a way to approach it ?

Thanks in advance.

Posted 23 January 2017 - 09:26 PM

Well numerical integration will just give you a numerical area, and I suppose that you want a plot of the primitive?

If you differentiate your equation that will turn it into a differential equation.

You can then create the plots by one of several numerical methods starting from the (presumably known) boundary conditions.

Edit A thought occurred to me

When you wrote this

I'm trying to find a primitive of f(x)=cos(-Asin(x)) where A is a constant number.

Did you mean the formula is the derivative of the function?

That is did you mean f'(x)=cos(-Asin(x)) ?

In which case you already have a differential equation to work on.

**Edited by studiot, 23 January 2017 - 11:42 PM.**

Posted 5 February 2017 - 01:10 PM

Hello Studiot,

Thanks for your kind contribution. Ideally, I'm after a function of A in order to plot it, knowing that I know between what values (O and Pi) I need to integrate this function. Actually, I asked for the primitive in order to calculate the integral, which is also a function of A, and this is the one I'd like to plot.

For your information, this primitive/integral is needed too solve Bessel's equation and function.

I'm sorry for the poor quality of my English.

Kind Regards.

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