The discussion revolves around integrating the Dirac Delta function within the context of a definite integral involving the expression (t-1) and a transformation of the variable t. Participants are exploring the implications of the Dirac Delta function in this integration process.
There are multiple interpretations of the integration approach being discussed, with some participants suggesting variable changes to simplify the problem. Guidance has been offered regarding the need to be cautious with the transformations involved in the integration process.
Participants are noting the importance of correctly applying the properties of the Dirac Delta function and the potential pitfalls in changing variables, particularly regarding the relationship between differentials.
Bugeye said:Homework Statement
I am trying to integrate the function
\int _{-\infty }^{\infty }(t-1)\delta\left[\frac{2}{3}t-\frac{3}{2}\right]dt
Homework Equations
The Attempt at a Solution
I think the answer should be \frac{5}{4} because \frac{2}{3}t-\frac{3}{2}=0 when t=9/4. then (9/4-1) = 5/4. However, when I put the equation into Mathematica, it gives me an anser of 15/8.
Bugeye said:Homework Statement
I am trying to integrate the function
\int _{-\infty }^{\infty }(t-1)\delta\left[\frac{2}{3}t-\frac{3}{2}\right]dt
Homework Equations
The Attempt at a Solution
I think the answer should be \frac{5}{4} because \frac{2}{3}t-\frac{3}{2}=0 when t=9/4. then (9/4-1) = 5/4. However, when I put the equation into Mathematica, it gives me an anser of 15/8.
Dick said:There's more to it than that. Do a change of variables u=2t/3-3/2. Don't forget du isn't the same as dt.