Applying the generalized divergence theorem to the set M X 1028 rN x a and , find the volume of Sn 1 x 1028 Rn x 1 in terms of the dimensional volume of Bn x 1028 Rn x 1 (This volume is n 2 (n 2) if is even and 2(n 1) 2 (n 1) 2 135 N if is odd ) ...

One has and since the outward ...

Applying the generalized divergence theorem to the set M = {XЄrN: |x| < a} and , find

Question:

Applying the generalized divergence theorem to the set M = {XЄrN: |x| < a} and , find the volume of Sn – 1 = {xЄRn: |x| = 1} in terms of the -dimensional volume of Bn = {x Є Rn: |x| <1}. (This volume is π n/2 / (n/2)! if is even and 2(n+1)/2π (n-1)/2 1∙3∙5∙. ∙ N if is odd.)