# Laplace Transform

1. Jun 22, 2011

### Precursor

The problem statement, all variables and given/known data
If $f(t)=K + 2cost$ and F(s) = L{f(t)}, find all the real values of $K$ such that $\int_{1}^{2}F(s)ds = 2ln5$

The attempt at a solution
So L{f(t)} = L{K} + L{2cost} = (K/s) + [2/(s2 + 1)]

So $$\int_{1}^{2}\frac{K}{s}ds + \int_{1}^{2}\frac{2s}{s^{s}+1}ds = 2ln5$$

After integration(I used integration by substitution for the second integral) and simplification, I get K(ln2) + ln(2) = 2ln(5)

Finally, I get K = [ln 25 - ln2]/ln2

Is this correct?

Last edited: Jun 22, 2011
2. Jun 22, 2011

### timthereaper

The second term in your equation is supposed to be ln(5). Using your method, I get K = 1+ln(5)/ln(2) or ln(10)/ln(2). But I don't see a problem with your method.

3. Jun 22, 2011

### vela

Staff Emeritus
Just doing this in my head, but I think the second integral evaluates to log(5/2).

4. Jun 22, 2011

### Precursor

I forgot to change the limits of integration when I used the method of substitution.