Calculus HELP!

posted by .

Use the fact that L{f'}=sF-f(0) to derive the formula for L{cosh at}

  • Calculus HELP! -

    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)}(1-s^2/a^2) = -s/a
    = (s/a^2)/(s^2/a^2 - 1)
    = s/(s^2-a^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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Posted by Aletha on Sunday, March 18, 2007 at 6:51pm. After t hours of an 8-hour trip the distance a car travels is modeled by: D(t)= 10t + (5)/(1+t) - 5 where D(t) is measured in meters. a) derive a formula for the velocity of the …
  2. calculus

    what is the anti-derivative on square root of cosh^2(x)?
  3. AP Physics

    I'm trying to derive the formula v^2 = v0^2 + 2a(x-x0) were zeros are subscripts my book tells me to derive it this way use the definition of average velocity to derive a formula for x use the formula for average velocity when constant …
  4. Physics PLEASE

    I'm trying to derive the formula v^2 = v0^2 + 2a(x-x0) were zeros are subscripts my book tells me to derive it this way use the definition of average velocity to derive a formula for x use the formula for average velocity when constant …
  5. Calculus

    Let y(x)=ln(cosh(x)+ sqrt(cosh^2(x)−1)) Find the derivative Dxy= I don't know what to do with this...
  6. Calculus Please Help

    Let y(x)=ln(cosh(x)+ sqrt(cosh^2(x)−1)) Find the derivative Dxy= I don't know what to do with this...
  7. Calculus

    Let y(x)=ln(cosh(x)+ sqrt(cosh^2(x)−1)) Find the derivative Dxy= I don't know what to do with this...
  8. calculus

    definite integral of (e^(8x))cosh(8x)dx from 0 to 1/16 -I substitued the definition of cosh in, i.e. (e^(8x) + e^(-8x)/2 but i cant get the "e's" to combine and i know the answer is e/32
  9. Calculus 1

    Find the numerical value of each expression. (Round your answers to five decimal places.) (a) cosh 9 (b) cosh(ln 9)
  10. Calculus

    How to derive cosh (3x) in terms of cosh (x) and sinh (x) ?

More Similar Questions