# Connection between unilateral laplace

1. May 4, 2014

### Jhenrique

Exist some conection between: $$\int_{0}^{+\infty} f(t) \exp(-st)dt\;\;(1)$$ $$\int_{-\infty}^{0} f(t) \exp(-st)dt\;\;(2)$$ ?

The results, the transformations, are very similar, with some little difference in the signal. So, known the transformation (1), is possible to find the (2)?

2. May 5, 2014

### Staff: Mentor

Where did you see the second equation above? The first one is the definition of the Laplace transform of a function f.

3. May 5, 2014

### lurflurf

^There is a bilateral Laplace transform that is the sum of the two unilateral Laplace transforms.
$$\int_{-\infty}^\infty \! \mathrm{f}(t)e^{-s \, t} \, \mathrm{d}x=\int_{-\infty}^0 \! \mathrm{f}(t)e^{-s \, t} \, \mathrm{d}x+\int_{0}^\infty \! \mathrm{f}(t)e^{-s \, t} \, \mathrm{d}x$$

Obviously in general we can say nothing about the two integrals. The function can be totally different for positive and negative values.