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# Delta Function with Trig Argument watch

1. Hi there..

I'm attempting to solve this problem

-pi/2 pi/2 exp(x) δ(cos(2x)) dx

Ive not seen an example of a delta function before where the argument isnt just an x-x'. For this I thought you'd just set the delta function to 0 giving a value of x=pi/4 or x=-pi/4 but Im not sure how you deal with the fact that there are two acceptable solutions?

Any help is greatly appreciated.

Thanks
2. (Original post by Eremor)
Hi there..

I'm attempting to solve this problem

-pi/2pi/2 exp(x) δ(cos(2x)) dx

Ive not seen an example of a delta function before where the argument isnt just an x-x'. For this I thought you'd just set the delta function to 0 giving a value of x=pi/4 or x=-pi/4 but Im not sure how you deal with the fact that there are two acceptable solutions?

Any help is greatly appreciated.

Thanks
Look at the Wikipedia article on the delta function.

It's the section called Composition with a Function
3. I assume youre referring to this relation?

What would xo be in this case though? Is it pi/4 or?

With there being two solutions (or not if im on the wrong path) am I correct in thinking you sum them to obtain the full answer perphaps?
4. (Original post by AbbieActon)
I assume youre referring to this relation?

What would xo be in this case though? Is it pi/4 or?

With there being two solutions (or not if im on the wrong path) am I correct in thinking you sum them to obtain the full answer perphaps?
The article discusses this and yes it's a sum over the roots.
5. Oh, my apologies didnt read the next bit down. Thankyou very much for all the help!

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