Learning Goal: I’m working on a applied mathematics multi-part question and need an explanation and answer to help me learn.
Solve the questions below ,References in APA format
1) Represent 𝒇(𝒙) = 𝐬𝐢𝐧 𝒙 𝒊𝒇 𝟎 < 𝒙 < 𝝅 and 0 if 𝒙 > 𝝅 as the Fourier Cosine Integral.
2) Represent 𝒇(𝒙) = 𝐜𝐨𝐬 𝒙 𝒊𝒇 𝟎 < 𝒙 < 𝝅 and 0 if 𝒙 > 𝝅 as the Fourier Sine Integral.
3) Find the Fourier Sine transform of 𝒇(𝒙) = 𝒙 𝟐 𝒊𝒇 𝟎 < 𝒙 < 𝟏 and 0 if 𝒙 > 𝟏.
4) Find the Fourier transform of 𝒇(𝒙) = 𝒆 −|𝒙| for −∞ < 𝒙 < ∞