- #1
Pual Black
- 92
- 1
Homework Statement
hi
i have to find the result of
##\int_{0}^{\pi}[\delta(cos\theta-1)+ \delta(cos\theta+1)]sin\theta d\theta##
Homework Equations
i know from Dirac Delta Function that
##\int \delta(x-a)dx=1##
if the region includes x=a and zero otherwise
The Attempt at a Solution
first i make the substitution
let ##\cos\theta=x##
then ##\sin\theta d\theta=-dx##
at ##\theta=0 \rightarrow x=1##
at ##\theta=\pi \rightarrow x=-1##
##\int_{1}^{-1}[\delta(x-1)+ \delta(x+1)](-dx)##
##\int_{-1}^{1}[\delta(x-1)+ \delta(x+1)](dx)##
##\int_{-1}^{1}\delta(x-1)dx+ \int_{-1}^{1}\delta(x+1)(dx)##
so the first term is equal one but what about the second term. I know that the result must be 2