Uploaded February 2026 | Updated September 2026, 2 weeks ago
We will find the volume of a 4d sphere using a quadruple integral! This is called a hypersphere and has the equation x^2+y^2+z^2+w^2=R^2. And yes, there's also the hyperspherical coordinates that we could use, but I will do that in a future video. Read more on en.wikipedia.org/wiki/N-sphere
๐ Shop my math t-shirts & hoodies: ๐ amzn.to/3qBeuw6
๐ Support this channel and get more content patreon.com/blackpenredpen
#blackpenredpen #calculus
We will find the volume of a 4d sphere using a quadruple integral! This is called a hypersphere and has the equation x^2+y^2+z^2+w^2=R^2. And yes, there's also the hyperspherical coordinates that we could use, but I will do that in a future video. Read more on en.wikipedia.org/wiki/N-sphere
๐ Shop my math t-shirts & hoodies: ๐ amzn.to/3qBeuw6
๐ Support this channel and get more content patreon.com/blackpenredpen
#blackpenredpen #calculus










