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1. Prove: Let F(t) = 1. Prove L[1] = 1/s , s > 0.

Proof.

2. Prove: Let F(t) = t. Prove L[t] = 1/s^{2} , s > 0.

Proof. In the proof we will use the following formula from a table of integrals (obtainable by integration by parts):

From the definition of a Laplace transform we have

3. Prove:

Proof.

Prove:

Proof. In the proof we will use the following formulas from a table of integrals:

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