- #1

warhammer

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- Homework Statement
- If F(k)= A(a+k) for -a<k<0

= A(a-k) for 0<k<a

= 0 for |x| > a

then calculate ##f(x)=\frac{A}{\sqrt{2π}} \int_{-a}^0 (a+k)e^{-ikx}\,dx + \int_0^a (a-k)e^{ikx}\,dx##

- Relevant Equations
- ##f(x)=\frac{A}{\sqrt{2π}} \int_-a^0 (a+k)e^{-ikx}\,dx + \int_0^a (a-k)e^{ikx}\,dx##

My Professor has started on the Fourier Transforms Topic in the Introductory Mathematical Physics class and gave us a small homework to try our concepts on.

I have attached a clear & legible snippet of my solution. I request someone to please have a look at it & determine if my solution is correct. (I'd also request some patience since this is my first dabble with the topic).

In the snippet, as described, I took the terms having 'i' as zero from a bit of assumed trickery, using the fact that F(k) had no terms having i as a coefficient so it must be zero in case of f(x) as well. (Not sure if this is correct way).

Then I solved for both integrals separately & added them after plugging in the desired limits.

(Edit 1- I'm fixing up on the Latex commands that I've written, please give a few moments, new to this actually.)

I have attached a clear & legible snippet of my solution. I request someone to please have a look at it & determine if my solution is correct. (I'd also request some patience since this is my first dabble with the topic).

In the snippet, as described, I took the terms having 'i' as zero from a bit of assumed trickery, using the fact that F(k) had no terms having i as a coefficient so it must be zero in case of f(x) as well. (Not sure if this is correct way).

Then I solved for both integrals separately & added them after plugging in the desired limits.

(Edit 1- I'm fixing up on the Latex commands that I've written, please give a few moments, new to this actually.)

**Mentor note**: I fixed up the broken LaTeX.#### Attachments

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