Problem in Matlab:"int(Dirac(x),x,-1,1)" =0 ???

[yannik33]

Hallo,
I computed in Matlab
"syms x"
"int(Dirac(x),x,-1,1)" and Matlab's solution is "0"?
What is the problem? (According to my knowledge the solution should be 1).

By the way, How can I calculate the integral(Dirac(x)^2) by hand (that was my objective), Thanks

 

[_Eduardo_]

Try dirac instead Dirac (lower case)

 

[blooz]

As Eduardo said ,it works

syms x 
>> int(dirac(x),x,-1,1)
 
ans =
 
1

 

[albbg]

To calculate the integral of dirac(x)^2 I think you can start from a constant function of amplitude 1/ε in a range -ε/2, +ε/2 and zero elsewhere. The δ(x) can be seen as the limit of such a function for ε\[\to\]0.
Then the integral from -∞ to +∞ of δ(x) will be the same of the integral taken from -ε/2 and +ε/2 and correspond to the integral of a constant value calculated between those two extremes:

lim(ε\[\to\]0) [1/ε•(ε/2+ε/2)] = 1

Considering now δ(2)², the range -ε/2, +ε/2 will remain the same while the height of the pulse will be (1/ε)² then the integral will be:

lim(ε\[\to\]0) [1/岕(ε/2+ε/2)] = +∞