# Quick convolution integral checking

1. Apr 8, 2007

### dfx

1. The problem statement, all variables and given/known data

Consider a linear system with the impulse response:

g(t) = $$3x^2 - 4x + 7$$ for t>0 and 0 otherwise.

Find the output for the input f(t) = t for $$t \geq 0$$ and f(t) = 0 for t<0.

2. Relevant equations

$$$\int_{-\infty}^t f(t - \tau)g(\tau)\,d\tau$$$

3. The attempt at a solution

$$$\int_0^t f(t - \tau)g(\tau)\,d\tau$$$

$$\[ \int_0^t (t - \tau)(3\tau^2 - 4\tau + 7\,d\tau\)]$$

and the answer I keep getting is

$$\frac{t^4}{4} - \frac{2t^3}{3} + \frac{7t^2}{2}$$

whereas the official given answer has the sign in the middle term as a plus: $$+\frac{2t^3}{3}$$

I've even tried wolfram and I think I'm correct:

http://img58.imageshack.us/img58/8637/mspzk2.gif [Broken] (obviously with different variables - x instead of tau, but still evaluted between t and 0).

If anyone could clear up the correct answer that would be much appreciated.

Last edited by a moderator: May 2, 2017
2. Apr 9, 2007

...anyone?

3. Apr 9, 2007

### Vagrant

Even I got the same answer as you. So I guess not much of a help.