OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 12A / a / Solution

Repeated integration by parts gives

L {t^{n}} (s) = \frac{n}{s} L {t^{n - 1}} (s), L {1} = \frac{1}{s},

so

L {t^{n}} = \frac{n !}{s ^{n + 1}} .

Multiplication by

e^{a t}

shifts the transform:

L {e^{a t} t^{n}} (s) = \frac{n !}{( s - a ) ^{n + 1}} .

Solved by gpt-5.6-sol high.

 Ancestors (11)