Why Does the Integration of exp[abs(x)+3]*delta(x-2) from -1 to 1 Equal Zero?

[NeedPhyHelp]

Homework Statement

Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1

2. The attempt at a solution

f(x)=exp[abs(x)+3]*delta(x-2)
f(2)=148.4
Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1 = 0

3. Why is the answer 0?

 

[Hootenanny]

Homework Statement

Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1

2. The attempt at a solution

f(x)=exp[abs(x)+3]*delta(x-2)
f(2)=148.4
Integrate exp[abs(x)+3]*delta(x-2) dx, -1, 1 = 0

3. Why is the answer 0?

Because the point x=2 does not lie in your domain of integration and your integrand vanishes at every other point.

 

[bilt7am]

Note that dirac delta function is zero if its argument is nonzero. The integration interval <-1;1> does not contain point x=2, where the dirac delta function is only nonzero.