Question

The Laplace transform of \[ \int_{0}^{t} p\sin(t-p)\,dp \] is

• A. \(\dfrac{s}{s^2+1}\)
• B. \(\dfrac{s+1}{s^2+1}\)
• C. \(\dfrac{1}{s}-\dfrac{s}{s^2+1}\)
• D. \(\dfrac{1}{(s-1)(s+1)}\)

Hint:

If \[ (f*g)(t)=\int_0^t f(p)g(t-p)\,dp, \] then \[ \boxed{ \mathcal{L}\{f*g\} = \mathcal{L}\{f\}\, \mathcal{L}\{g\}. } \] This is known as the Convolution Theorem.

Answer 1

The Correct Option is C