# The Fourier Integral (Q#2)

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 < ∞

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