SUBSTITUTION in MULTIPLE INTEGRALS

Question

darkprince14 · Answer

attachment

perl · Answer

the equation of the hypersphere will be 
 
w = sqrt( R^2 - (x^2 + y^2 + z^2))

darkprince14 · Answer

I don't know how to plug them in. I haven't researched yet the function formula of a hypersphere. I tried determining Jacobians and ended up with R and rho

perl · Answer

x^2 + y^2 = ( r cos t )^2 + (r sin t)^2 = r^2 ( cos^2 t + sin^2 t) = r^2

darkprince14 · Answer

$$w ^{2} \le \sqrt{R ^{2}-(x ^{2}+y ^{2}+z ^{2})}$$$$w ^{2} \le \sqrt{R ^{2}-(r ^{2}+z ^{2})}$$
then...

darkprince14 · Answer

it's w^2. It should be w alone, sorry for that..

darkprince14 · Answer

it's not w^2

perl · Answer

this is a good resource but some of the images are not showing http://cr4.globalspec.com/blogentry/1075/Hyperspheres-Part-I-The-4-Dimensional-Hypersphere

perl · Answer

can you fill in the missing blanks this is also good http://peeterjoot.wordpress.com/2013/01/27/hypersphere-volume-calculation-the-easy-way/