Find the Laplace transform of Solution We can rewrite the above function like so f(t) = (t2-8t+20)u(t-4) f(t) = t2 u(t-4)- 8tu(t-4) + 20u(t-4) Now we need to apply a trick and subtract and add 4 f(t) = (t-4+4)2u(t-4)- 8(t-4+4)u(t-4) + 20u(t-4) f(t) = (t-4)2u(t-4)+8(t-4)u(t-4)+ 16u(t-4) - 8(t-4)u(t-4) -32u(t-4)+ 20u(t-4) f(t) = (t-4)2u(t-4) + 4u(t-4) Now we can take the laplace transform F(s) = 2e-4s/s3 + 4e-4s/s.

1. Find the Laplace transform of
Solution
We can rewrite the above function like so
f(t) = (t2-8t+20)u(t-4)
f(t) = t2 u(t-4)- 8tu(t-4) + 20u(t-4)
Now we need to apply a trick and subtract and add 4
f(t) = (t-4+4)2u(t-4)- 8(t-4+4)u(t-4) + 20u(t-4)
f(t) = (t-4)2u(t-4)+8(t-4)u(t-4)+ 16u(t-4) - 8(t-4)u(t-4) -32u(t-4)+ 20u(t-4)
f(t) = (t-4)2u(t-4) + 4u(t-4)
Now we can take the laplace transform
F(s) = 2e-4s/s3 + 4e-4s/s