Question

Integrate

Answer 1

\[\int\limits_{0}^{\infty} (sint/t)\delta (t-\pi/6)dt\]

Answer 2

\(\Large \int \limits _{-\infty}^\infty f(x)\delta(x)\, dx = f(0)\)

what does this tells us ? for every value of x, other than x=0, since \(\delta(x)=0\), we only have the non-0 product at x=0


in same way,
\(\int\limits_{0}^{\infty} (\sin t/t)\delta (t-\pi/6)dt\)
we only have non-0 product at t = pi/6

\(\Large \int\limits_{0}^{\infty} (\sin t/t)\delta (t-\pi/6)dt = \sin(\pi/6)/(\pi/6) =...\)

Answer 3

I don't get it at all, that sigma threw me out.

Answer 4

what sigma?

Answer 5

its not sigma
\(\large \delta ~ is ~ Delta\)
which is Dirac Delta function
http://en.wikipedia.org/wiki/Dirac_delta_function