Question

4. Using the properties of the Fourier transform, evaluate the following integrals in terms of a and/or 6, where a is positive. You have to express real-valued evaluations. eat sinc(t)dt -nt - atcos (Bt)dt (10 pts) (a) (10 pts) (b) e 0 0 d [In (x)] dx Hint: teldt -1디미플

Answer 1

As the limits of the integrals are from 0 to $\infty$ so instead of Fourier transform,, e can use Laplace transform.

As nc lt) Ain lt) t Oc 1-fEe int dt t 0 Cemider st mt dt t eLi 4mt2 LiSmt ds tems
So the anser is obtained when
S
.

Thus

-tan 1 I 2

b)

1-JEE t CAt) dt e Cess Agair hote hat st Cess e 0 Ces 2 , 2 11