9.8. Dirichlet’s Integral

Try these first

1. 1.

   What is Dirichlet's Integral when x > 0?

   Hint

   Recall the first condition of the integral evaluation.

2. 2.

   For which value of x does Dirichlet's Integral evaluate to zero?

   Hint

   Think about what happens at the origin in the integral evaluation.

3. 3.

   What is the value of Dirichlet's Integral when x equals zero?

   • 0
   • π/2
   • -π/2

   Hint

   Think about the integral's behavior at the origin.

4. 4.

   True or False: Dirichlet's Integral can be used for both sine and cosine functions.

   • True
   • False

   Hint

   Recall what Dirichlet's Integral encompasses.

5. 5.

   Given a material that is subjected to varying loads, how would you apply Dirichlet's Integral in analyzing the stress distribution?

   Hint

   Consider methods of integrating over the applied loads.

6. 6.

   Integrate Dirichlet's Integral from -∞ to ∞ for a different function to understand its behavior under alteration.

   Hint

   Adjust according to the given boundary conditions.