9.4. Fourier Cosine and Sine Integrals

Try these first

1. 1.

   What form does the Fourier integral take for an even function?

   Hint

   Remember, even functions only use cosine terms!

2. 2.

   How do you express a Fourier integral for an odd function?

   Hint

   Focus on sine terms for odd functions!

3. 3.

   What type of function does the Fourier Cosine Integral represent?

   • Odd
   • Even
   • Neither

   Hint

   Think about the symmetry of the functions.

4. 4.

   True or False: The Fourier Sine Integral contains only cosine terms.

   • True
   • False

   Hint

   Consider what type of functions lead to each integral.

5. 5.

   Given an even piecewise function defined as f(x)=3 for -1 < x < 1, find the Fourier cosine integral representation.

   Hint

   Use the properties of even functions and calculate carefully.

6. 6.

   For an odd function defined in intervals, analyze and produce its Fourier sine integral representation.

   Hint

   Focus on the integration limits and properties of odd functions.