Derive a formula for the volume of a d-dimensional hypersphere.
Step 1 of 3
The Gaussian function has an antiderivative and if it is integrated from to , its numerical value is found to be
If the function is squared and double integration is done on it. The square is values as .
The expression for area of a d-dimensional hypersphere is given as,
The volume of segment that is unit thick is given by,
Integrating this expression,
This is the formula for the volume of a d-dimensional hypersphere.
Textbook: An Introduction to Thermal Physics
Author: Daniel V. Schroeder
This textbook survival guide was created for the textbook: An Introduction to Thermal Physics , edition: 1. The full step-by-step solution to problem: 16P from chapter: B was answered by , our top Physics solution expert on 07/05/17, 04:29AM. The answer to “Derive a formula for the volume of a d-dimensional hypersphere.” is broken down into a number of easy to follow steps, and 10 words. This full solution covers the following key subjects: derive, Dimensional, formula, hypersphere, Volume. This expansive textbook survival guide covers 10 chapters, and 455 solutions. An Introduction to Thermal Physics was written by and is associated to the ISBN: 9780201380279. Since the solution to 16P from B chapter was answered, more than 380 students have viewed the full step-by-step answer.