Mathematics · University
Laplace transform of a monomial
This transform integrates over t ≥ 0. Substitute a positive s after transforming.
Method and conditions
This transform integrates over t ≥ 0. Substitute a positive s after transforming.
L{tⁿ}(s) = n!/s^(n+1), s>0
Worked examples
Find the Laplace transform of 2t^5, then evaluate it at s = 7. Round the final result to 4 decimal places if needed.
The transform is 2(5!)/s^6. Substitute s = 7.
0.002
Find the Laplace transform of 16t^7, then evaluate it at s = 8. Round the final result to 4 decimal places if needed.
The transform is 16(7!)/s^8. Substitute s = 8.
0.0048
Try it
Find the Laplace transform of 3t^6, then evaluate it at s = 8. Round the final result to 4 decimal places if needed.
Find the Laplace transform of 18t^3, then evaluate it at s = 5. Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 0.001
The transform is 3(6!)/s^7. Substitute s = 8.
- 0.1728
The transform is 18(3!)/s^4. Substitute s = 5.
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