00:01
In this question, we need to find the bilateral laplace transform and radius of curvature of the following function, which is x of t is equals to u times t plus 2, e raised 2 minus 3, t plus 2 plus 2 plus 7 u times minus t minus 5, e raise 2, 4 times minus minus 5.
00:25
We have to find the bilateral laplace transform okay so we know that the laplace transform is defined by x of s is equals to minus infinity to infinity e raise to minus s t x of t d t so from this what i get x of s to be equals to minus infinity to infinity e raise to minus s t okay so we are applying the laplace transform to the given function okay so we get the following u of t plus 2 e raise 2 minus 3 times t plus 2 d t plus integral minus infinity e raise to minus st 7 u of minus t minus 5 e raised to 4 times minus t minus 5 d t correct so we can simplify it one step further so this becomes e raise 2 minus 6 and this will be integral from minus 2 to infinity, e raised to minus s plus three times of t, t, t plus from here we can take 7e raised to minus 20 out.
01:43
We are left with minus infinity to minus 5, e raised to minus of s plus 4 times of t, dt.
01:53
Correct.
01:55
So from this what i will say, x of s is equals to e raise to minus 6.
02:00
Integral here will be e raised to minus s plus three times of t over minus of s plus three, correct? limit from minus 2 to infinity plus 7, e raise to minus 20.
02:16
Here integral is e raised to minus s plus 4 times of t over minus of s plus 4, correct.
02:26
Limit is from minus infinity to 5...