Calculate between [-epsilon,epsilon]

  • #1
i need to integrate

[tex]-(p(y)f(y)')'=m^2w(y)f(y)[/tex]
where
[tex]p(y)=e^{4ky}(1-4ak^2)[/tex] and [tex]w=-4ae^{2y}k\delta(y)[/tex]

but y between [0,infinity[

¿i calculate between [tex]\int^{epsilon}_0????[/tex] or ¿i calculate between [-epsilon,epsilon]?????

but, what is??

[tex]\int^{\epsilon}_0(p(y)f(y)')'dy[/tex]

whit f is not continuous in zero


the result is
[tex]f(+\epsilon)=-\frac{m^24akf(0)}{1-4ak^2}[/tex]
 
Last edited:

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,833
956


i need to integrate

[tex]-(p(y)f(y)')'=m^2w(y)f(y)[/tex]
where
[tex]p(y)=e^{4ky}(1-4ak^2)[/tex] and [tex]w=-4ae^{2y}k\delta(y)[/tex]

but y between [0,infinity[

¿i calculate between [tex]\int^{epsilon}_0????[/tex] or ¿i calculate between [-epsilon,epsilon]?????
I have no idea what you are talking about. What are yu integrating? If you are talking about the integral above, if it is given as a definite integral, you use whatever limits of integration are given. If it is given as an indefinite integral (anti-derivative) you do not use any limits of integration.

but, what is??

[tex]\int^{\epsilon}_0(p(y)f(y)')'dy[/tex]
By the Fundamental Theorem of Calculus, the integral of the derivative of any function is that function:
[tex]\int^{\epsilon}_0(p(y)f(y)')'dy= p(y)f(y)' [/tex]


whit f is not continuous in zero
If f is not continuous at zero, then it is not differentiable at zero and the integrand above does not exist at 0.


the result is
f(+\epsilon)=-\frac{m^24akf(0)}{1-4ak^2}
Since you haven't actually stated what the problem is, I have no idea whether that is correct or not.
 
  • #3
Last edited by a moderator:

Related Threads on Calculate between [-epsilon,epsilon]

  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
5
Views
11K
  • Last Post
Replies
4
Views
8K
Replies
2
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
31
Views
9K
  • Last Post
Replies
2
Views
3K
Replies
1
Views
2K
Top