The document discusses integration of transforms. It defines an integral transform as a mapping of a function from its original function space to another function space via integration, where some properties of the original function may be more easily characterized and manipulated. The transformed function can generally be mapped back to the original function space using the inverse transform. It provides the definition of the Laplace transform and uses examples to illustrate applying the definition.

1. INTEGRATION OF
TRANSFORMS
By:
MUGESH M(2020504017)

2. INTEGRATION OF
TRANSFORMS
● An integral transform maps a function from its original function
space into another function space via integration, where some of
the properties of the original function might be more easily
characterized and manipulated than in the original function space.
● The transformed function can generally be mapped back to the
original function space using the inverse transform.

3. DEFINITION
By the definition of Laplace transform,
● If L{ f (t)} = F(s), then,

4. Proof:

5. Example 1:

6. Solution:

7. Example 2:

8. THANK YOU