Average of function (using dirac delta function)

[j3dwards]

Homework Statement

Compute the average value of the function:

f(x) = δ(x-1)*16x²sin(πx/2)*e^iπx/(1+x)(2-x)

over the interval x ∈ [0, 8]. Note that δ(x) is the Dirac δ-function, and exp(iπ) = −1.

Homework Equations

∫ dx δ(x-y) f(x) = f(y)

The Attempt at a Solution

Average of f(x) = 1/8 ∫from 0 to 8 δ(x-1) dx 16x²sin(πx/2)*(-1)/(1+x)(2-x)
Average of f(x) = -1

Is this correct? I'm unsure of whether you can just use δ(x-a) = δ(x-1) and let a=1 and not let a=-1? I don't get how to use this bit of the function as I seem to have just ignored the negative sign.

Many thanks.

 

[nuclear_chris]

From the problem statement, your a is = to 1 not -1.