# Integrating a dirac-delta

1. Jan 30, 2012

### zheng89120

1. The problem statement, all variables and given/known data

Show:

02∏ δ(sin θ - k) dθ

equals

θ(1-|k|) * 2/sqrt(1-k2)

2. Relevant equations

integrating dirac-delta function

3. The attempt at a solution

[sin (2pi) - k] - [sin 0 - k] ??

Last edited: Jan 30, 2012
2. Jan 30, 2012

### lanedance

now I'm assuming the second theta is actually a heaviside function (some bad choice of notation but surprisingly to a few other recent posts)

as for your answer it doesn't make a heap of sense, what do you actually know about integrating the delta function...

Last edited: Jan 30, 2012
3. Jan 30, 2012

### lanedance

first consider when |k| > 1,what is the value of the integral...?

4. Jan 30, 2012

### lanedance

now when |k| < 1, i would try a substitution... and ask yourself again what do you actually know about integrating the delta function?

the form of the answer may also give u a hint, though I haven't fully worked it through... what common function f(k) integrates to 1/(1-k^2)?

5. Jan 31, 2012

### zheng89120

I am not sure how to integrate dirac-delta of a polynomial such as [sin(theta) - k] unfortunately.

6. Jan 31, 2012

### HallsofIvy

Do you know what $\int_a^b \delta(x) dx$ itself is?

7. Jan 31, 2012

### lanedance

exactly start from what you do know

8. Jan 31, 2012

### lanedance

also that is not a polynomial

9. Jan 31, 2012

### lanedance

Once you can answer that ask the following questions, how do you solve
$\int_a^b \delta(2x) dx$

then
$\int_a^b \delta(2x-k) dx$

and what is the value of
$\int_a^b \delta(2x-k) f(x) dx$

If you can do those you shoudl have a pretty good idea how to do approach the problem, along with some trig and you should be there

10. Jan 31, 2012

### zheng89120

okay, i think i got it, or at least as long as I am assuming a trig identity correctly, much thanks

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