1. Mathematics
2. Geometry and Topology
3. Analytic Geometry
4. Trigonometry
5. 17383

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Please do #4.

Please see the attached file for full problem description.

In this project, we find formulas for the enclosed by a hypersphere in n?dimensional spaces
1 Use a double integral, and trigonometric substitution, together with Formula 64 in the Table of Integrals, to find the area of a circle with radius r

2 Use a triple integral and trigonometric substitution to find the volume of a sphere with radius r.

3 Use a quadruple integral to find the hypervolume enclosed by the hypersphere.....
(Use only trigonometric substitution and the reduction formulas for....

4 Use an n-tuple integral to find, the volume enclosed by a hypersphere of radius r in
n-dimensionai space R [Hint: The formulas for n even and for n odd are different.]