integral of product of curve with itself in three dimensional

Question

I have the next problem:

Let $\gamma:[0,1]\to R^3$ differentiable curve piecewise, and let $\Delta_r=\{(s,t)\in [0,1]^2| |\gamma(s)-\gamma(t)|<r\}$, i want to know if:

$$\int_{\gamma\times\gamma\cap \Delta_r}\gamma'(s)\gamma'(t)dsdt\geq 0 $$

I have the easy case when $r>diam(\gamma)$.

Thanks!