Question

find Laplace transform of function sint\t​

Answer 1

Answer:

Hope You Like It I Have tried my best though i m not good at maths

Step-by-step explanation:

a) Using the power series (Maclaurin) for sin(t)sin⁡(t) - Find the power series representation for f(t)f(t) for t>0.t>0.

b) Because f(t)f(t) is continuous on [0,∞)[0,∞) and clearly of exponential order, it has a Laplace transform. Using the result from part a) (assuming that linearity applies to an infinite sum) find L{f(t)}L{f(t)}. (Note: It can be shown that the series is good for s>1s>1)

There's a few more sub-problems, but I'd really like to focus on b).

I've been able to find the answer to a):

1−t23!+t45!−t67!+O(t8)

1−t23!+t45!−t67!+O(t8)

The problem is that I'm awful at anything involving power series. I have no idea how I'm supposed to continue here. I've tried using the definition of the Laplace Transform and solving the integral

∫∞0e−st∗sin(t)tdt

∫0∞e−st∗sin(t)tdt

However, I just end up with an unsolvable integral.