Fourier Sine And Cosine Integrals

FOURIER SINE AND COSINE INTEGRALS

1.(b) Problems based on Fourier cosine and Fourier sine integrals

Example 4.1.b(1): Find Fourier cosine integral of the function

Solution: We know that, the Fourier Cosine integral of f (x) is given by

Example 4.1.b(2): Using Fourier integral formula, show that

Solution: We know that, the Fourier Cosine integral of f (x) is given by

Example 4.1.b(4): Using the Fourier integral representation show that

Solution :

Example 4.1.b(5): Using Fourier integral formula, prove that 

Example 4.1.b(6): Applying the Fourier sine integral formula to the function