Integral

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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.

Kind Regards.

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Would a numerical integration method not do nicely?

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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.).

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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 ?

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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
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• 2 weeks later...

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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