Using the fourier integral show that Integration from 0 to infinity [(sinw coswx)/w]dw=pi/2 ||#viral

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Using fourier integral show that Integration from 0 to infinity [(cos wx)/(1+w^2)]dw=(pi/2)e^-x

Fourier integral representation show Integration from 0 to infinity [(wsin xw)/(1+w^2)]dw=(pi/2)e^-x

Fourier Integral

But what is the Fourier Transform? A visual introduction.

Fourier transform-3 Fourier cosine and sine transforms

Fourier Sine integral

Using Fourier integral representation, show that

Using Fourier integral representation, show that