Let $B(0,1) \subseteq \Bbb{R}^d$ the open unit ball and $x \in \Bbb{R^d}$ such that $|x|>1$.
Let the ball $B_x=B(\frac{1}{2}(|x|-\frac{1}{|x|})\frac{x}{|x|},\frac{1}{2}(|x|+\frac{1}{|x|}))$ in $\Bbb{R}^d$
We obsviously have $|x|+\frac{1}{|x|}>2$
How can i calculate the volume of $B_x \cap B(0,1)$?
Is there a general technique/formula and an article or pdf,for calculating these types of volumes?
Thank you in advance.