# Simple yet tricky definite integration problem!

1. Apr 12, 2013

### Tamis

I'm given:
$f(x)=\left\{\begin{matrix} 1 & -1\leq x \leq 1\\ 0 & otherwise \end{matrix}\right.$

The integral to evaluate is:
$\int_{-1}^1 f(x-t) dt$

What integration techniques should i use to solve this problem?
Could someone please provide the steps to solve this problem (as the answer only provides the solution, and not the steps)?

2. Apr 12, 2013

### drawar

I'm not sure if it really works, but let me just write it down:

Do the change of variable u=x-t then the integral becomes $\int\limits_{x - 1}^{x + 1} {f(u)du}$.
Now consider 4 cases:
(i) $x - 1 \le - 1 < 1 \le x + 1$
(ii)$- 1 \le x - 1 < 1 \le x + 1$
(iii)$x - 1 \le - 1 < x + 1 \le 1$
(iv)$- 1 \le x - 1 < x + 1 \le 1$

3. Apr 12, 2013

### Ray Vickson

Forum rules require you to show your work. Surely you can figure out most of this problem by yourself! Just think about what f(x-t) is for various x and t.