# A question on the Dirac delta distribution

user1139
Homework Statement:
Relevant Equations:
Is it correct to say that

$$\int e^{-i(k+k’)x}\,\mathrm{d}x$$

is proportional to ##\delta(k+k’)##?

$$\int \hat\phi(k) \int e^{-i(k+k')x} dx\, dk = \int e^{-ik'x} \int \hat\phi(k) e^{-ikx} dk\, dx = \int e^{-ik'x} \phi(-x) dx = \int e^{ik'x} \phi(x) dx = 2\pi \hat \phi(-k') = \int 2\pi \delta(k+k') \hat\phi(k) dk.$$