Set up an integral for finding the laplace transform of f(t)=t−6. f(s)=l{f(t)}=∫ba e^(-s*t)(t-6)dt equation editorequation editor (formulas) where a= 0 equation editorequation editor and b= inf equation editorequation editor . find the antiderivative (with constant term 0) corresponding to the previous part. equation editorequation editor evaluate appropriate limits to compute the laplace transform of f(t): f(s)=l{f(t)}= equation editorequation editor where does the laplace transform you found exist? in other words, what is the domain of f(s)? equation editorequation editor (inequalities)

See below

Step-by-step explanation:

By definition the Laplace transform of f(t) = t-6 is

To find an anti-derivative, let's consider the indefinite integral  

and use integration by parts.

If we set

then

hence

To find the Laplace transform we evaluate the improper integral as

But

and does not exist for s<0.

So, the Laplace transform only exists for s>0 and equals

for s>0

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4