Mathematics · University
Laplace transform of a monomial · formula reference
This transform integrates over t ≥ 0. Substitute a positive s after transforming.
Formula
This transform integrates over t ≥ 0. Substitute a positive s after transforming.
L{tⁿ}(s) = n!/s^(n+1), s>0
Worked example
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
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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