Fourier transforms | prove that the fourier transform of the function f(x)=e^-|x| is 2/(1+λ^2)

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In this video we are discussed basic problem of Fourier Transform. This video helpful to Engineering Students and also helpful to MSc/BSc/CSIR NET / GATE/IIT JAM students.

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1)Introduction and Definition of infinite Fourier Transform in Hindi,
2)Type of Fourier Transform
3)infinite Fourier Transform
4)The Finite Fourier transform
5)Fourier integral Transform
6)Inverse Fourier Transform
7)Complex Fourier Transform
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Find fourier cosine and sine transform of
function f(x)=e^(-mx)
Prove that
a.∫_0^∞〖cos⁡λx/(m^2+λ^2 ) dλ=π/2m〗 e^(-mx),
b. a.∫_0^∞〖〖λ sin〗⁡λx/(m^2+λ^2 ) dλ=π/2〗 e^(-mx),
Q.2) prove that fourier transform of function
f(x)=e^(-|x|) is 2/(1+λ^2 )