- #1
BOAS
- 552
- 19
Hello,
I feel like I am fudging these integrals a bit and would like some concrete guidance about what's going on.
1. Homework Statement
Evaluate ##I = \int_{-1}^{1} dx \delta'(x)e^3{x} ##
[/B]
I use integration by parts as follows,
##u = e^{3x}##
##du = 3e^{3x} dx##
##dv = \delta'(x)##
##v = \delta(x)##
##I = uv|^{1}_{-1} - \int^{1}_{-1} v du##
Evaluating ##uv## gives zero because the delta function is zero at both limits.
##I = - \int^{1}_{-1} dx \delta(x) 3e^{3x}##
Clearly, the only non zero value of this function is at ##x = 0##, making me think the answer to my problem is ##I = -3##, but this is the step that I think I'm 'fudging'. I feel like I'm disregarding the integration sign...
Is this justified?
Thanks for any guidance you can give.
I feel like I am fudging these integrals a bit and would like some concrete guidance about what's going on.
1. Homework Statement
Evaluate ##I = \int_{-1}^{1} dx \delta'(x)e^3{x} ##
Homework Equations
The Attempt at a Solution
[/B]
I use integration by parts as follows,
##u = e^{3x}##
##du = 3e^{3x} dx##
##dv = \delta'(x)##
##v = \delta(x)##
##I = uv|^{1}_{-1} - \int^{1}_{-1} v du##
Evaluating ##uv## gives zero because the delta function is zero at both limits.
##I = - \int^{1}_{-1} dx \delta(x) 3e^{3x}##
Clearly, the only non zero value of this function is at ##x = 0##, making me think the answer to my problem is ##I = -3##, but this is the step that I think I'm 'fudging'. I feel like I'm disregarding the integration sign...
Is this justified?
Thanks for any guidance you can give.