# Volume of the intersection of $n$-siplex and $n$-sphere

I want to calculate volume of the intersection of $$n$$-simplex $$\left\{ x_1,x_2, \ldots, x_n: \sum\limits_{i=1}^nx_i\leqslant 1, x_i\geqslant 0 \right\}$$ and $$n$$-sphere with center in $$\left( 1,0,0,\ldots, 0 \right)$$ and radius $$R \leqslant \frac{\sqrt{2}}{2}$$, but really has no idea how.