I have the following signals
https://i.stack.imgur.com/uP1Uo.jpg
where $A=10$ and $T=5\,ms$.
I have to check that the two signals are orthogonal, which means I have to solve
$<s_1(t),\,s_2(t)>=\int_{0}^{T}s_1(t)\cdot s_2(t)\,dt$
but I don't know how to get $s_1(t)$ and $s_2(t)$ in a form I'm able to integrate.
As suggested by @Alt (see comment above), the two signals are divided into $3$ intervals:
$\left[0,\,\frac{1}{3}T\right],\,\left[\frac{1}{3}T,\,\frac{2}{3}T\right],\,\left[\frac{2}{3}T,\,T\right]$
In those intervals $s_2(t)$ is
$A \iff T\in\left[0,\,\frac{1}{3}T\right]\cup\left[\frac{2}{3}T,\,T\right]$
$-A \iff T\in\left[\frac{1}{3}T,\,\frac{2}{3}T\right]$
$s_1(s)$ is therefore scaled by a factor of $A$ in the left and right triangles and a factor of $-A$ in the middle one. The middle triangle has a negative area which is equal (in absolute value) to the sum of the other two triangles and when all the areas are summed together (a.k.a. when the integral is calculated) the result is $0$:
$<s_1(t),\,s_2(t)>=\int_{0}^{T}s_1(t)\cdot s_2(t)\,dt=\frac{1}{6}TA^2-\frac{1}{3}TA^2+\frac{1}{6}TA^2=0$