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Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 4 / 12A / a / Solution

The Heaviside factor restricts the integral to

t \geq α

. With

u = t - α

,

L {f (t - α) H (t - α)} (s) = \int_{α}^{\infty} e^{- s t} f (t - α) d t = e^{- α s} \int_{0}^{\infty} e^{- s u} f (u) d u = e^{- α s} F (s) .

Solved by gpt-5.6-sol high.

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