6.5. Application in Solving Problems

Try these first

1. 1.

   What is the Laplace Transform of the integral of a constant function?

   Hint

   Think of how constants behave in integration.

2. 2.

   How does the theorem relate to continuous functions?

   Hint

   Consider the nature of the functions involved.

3. 3.

   What does the Laplace Transform of an integral equal?

   • F(s)
   • F(s)/s
   • sF(s)

   Hint

   Think about how integration behaves in the Laplace domain.

4. 4.

   True or False: The Laplace Transform only applies to continuous functions.

   • True
   • False

   Hint

   Consider the definition of continuity.

5. 5.

   Given f(t) = e^(-3t), find L{∫(from 0 to t) e^(-3τ) dτ}.

   Hint

   Start by finding the Laplace Transform of the exponential function.

6. 6.

   Evaluate L{∫(from 0 to t) sin(2τ) dτ} and explain the steps.

   Hint

   Break this problem into parts: identify functions and apply the theorem methodically.