How Do I Integrate Nested Trigonometric Functions?

In summary, the conversation discusses how to integrate sin[y*sin(x)]*sin(x) with limits from -pi to pi. It is mentioned that the function is even so the limits can be changed to 0 to pi and doubled, but the analytic answer cannot be found. Different methods such as integration by parts and substitution are suggested, but it is noted that there may not be an elementary anti-derivative for this function. The question arises if there is a standard method for integrating nested trig functions.
  • #1
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How do I go about integrating

sin[y*sin(x)]*sin(x) wrt x from -pi to pi,

I've got that its an even function so I can change the limits to 0 to pi and double it, but I can't find the analytic answer. By parts? substitution? although for substitution I assume there needs to be a cos function somewhere. Any ideas?

Thanks
 
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  • #2
So y is a constant here?

Do you have any reason to think that there IS an elementary anti-derivative? (Most functions do not.)
 
  • #3
Actually, I have no reason to believe it is doable. It came up in a proof I was working on involving some bessel function. I was just wondering if their was a standard method for nested trig functions.

Thanks for your time
 

FAQ: How Do I Integrate Nested Trigonometric Functions?

What are nested trig functions?

Nested trig functions refer to the use of one trigonometric function inside another trigonometric function, such as using sine inside cosine or tangent inside secant.

Why are nested trig functions important?

Nested trig functions allow for more complex mathematical calculations involving angles and sides of a triangle. They are also commonly used in physics and engineering applications.

What are some common examples of nested trig functions?

Some common examples include using the inverse sine function (arcsin) inside the cosine function (cos), or using the tangent function (tan) inside the secant function (sec).

How do you simplify nested trig functions?

To simplify nested trig functions, you can use trigonometric identities and properties. For example, you can use the double angle formula to simplify expressions with double nested trig functions.

What are some real-life applications of nested trig functions?

Nested trig functions are used in various fields such as astronomy, navigation, and architecture. For example, calculating the trajectory of a satellite or the height of a building often involves nested trig functions.

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