Question

Find the Laplace transform of f(t) = 3t^(5/2) + 4t^3.

Answer 1

so i get 4*3!/(s^4) but then i dont know how to figure out the first part hah

Answer 2

I think you just leave the 5/2! as is?

Answer 3

for the first part I get [3(5/2!)]/s^(3.5)

Answer 4

so then it would be 3(5/2)!/s^(7/2) ?

Answer 5

yup

Answer 6

alright i think im just confusing myself because the answer in the back of the book is more complex haha

Answer 7

Well, you can't techncally take factorial of fraction lol! I'd leave it like that :D

Answer 8

Try taking the integral from 0<t<∞

Answer 9

yeah i mean wolfram knows how but im clueless ha, the integral? hmm

Answer 10

maybe i can take the integral to simplify it and then go from there

Answer 11

So your problem is the (5/2)! not the laplace transform lol!

Answer 12

sorry i mean the gamma. isn't it the gamma that means to take the integral? i'm trying to remember. haha

Answer 13

yeah so its supposed to be 45pi - 192s^(3/2)/(8s^(7/2))

Answer 14

The gamma function is defined as:
\[\Gamma = \int\limits_{0}^{∞}e^{-x}x ^{t-1}dx\]

Answer 15

alright thanks :)