Calculate the Dirac delta function integral

[PeroK]

while solving the problem if we do such type of substitution then it is necessary to put a negative sign otherwise it will be wrong?

No. But, you were going to use:

(X) ##\int_{-1}^{1}\delta(x)dx = 1##

And, you were going to assume that the order of the limits doesn't matter. So, you were going to assume that:

##\int_1^{-1}\delta(x)dx = 1##

Which would be wrong. So, you have to get the limits in the right order before you apply equation (X).

Take a look at the first property of the definite integral here (half way down the page).

http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDefiniteIntegral.aspx

 

[Mark44]

Thread closed, as the OP is now banned.