Posted by Sara on Saturday, July 27, 2013 at 9:33pm.
Use the fact that L{f'}=sFf(0) to derive the formula for L{cosh at}

Calculus HELP!  Steve, Sunday, July 28, 2013 at 5:51am
cosh(at) = d/dt (1/a sinh(at))
sinh(at) = d/dt (1/a cosh(at))
So,
Since L{f(at)} = 1/a F(s/a)
L{cosh(at)} = sL{1/a sinh(t)}
= s/a L{sinh(t)}
L{sinh(at)} = sL{1/a cosh(at)}
= s/a L{cosh(at)}  s/a
So,
L{cosh(at)} = s/a (s/a L{cosh(at)}  s/a
L{cosh(at)}(1s^2/a^2) = s/a
= (s/a^2)/(s^2/a^2  1)
= s/(s^2a^2)
Better check my algebra in the middle steps. I think I dropped an "a" somewhere, but the final answer is correct. You work this in the same way you do integration by parts twice for trig functions.
Answer This Question
Related Questions
 Calculus  How to derive cosh (3x) in terms of cosh (x) and sinh (x) ? Initially...
 calculus  what is the antiderivative on square root of cosh^2(x)? The square ...
 calculus  definite integral of (e^(8x))cosh(8x)dx from 0 to 1/16 I substitued ...
 Calculus Please Help  Let y(x)=ln(cosh(x)+ sqrt(cosh^2(x)−1)) Find the ...
 Calculus  Let y(x)=ln(cosh(x)+ sqrt(cosh^2(x)−1)) Find the derivative Dxy...
 Calculus  Let y(x)=ln(cosh(x)+ sqrt(cosh^2(x)−1)) Find the derivative Dxy...
 Calculus 1  Find the numerical value of each expression. (Round your answers to...
 AP Physics  I'm trying to derive the formula v^2 = v0^2 + 2a(xx0) were zeros ...
 Physics PLEASE  I'm trying to derive the formula v^2 = v0^2 + 2a(xx0) were ...
 Calculus  Posted by Aletha on Sunday, March 18, 2007 at 6:51pm. After t hours ...
More Related Questions