Measuring volume of spheres using triple integrals

[robertjford80]

Homework Statement

I'm just interested in knowing where the 4 comes from in front of the integral.

 

[tiny-tim]

hi robertjford80!

that 4∫₀^π/2 is really ∫₀^2π …

i suppose the writer thought it looks confusingly like ∫₀⁰, though i see nothing wrong with it!

 

[robertjford80]

Ok, pretty unexpected but I guess it makes sense.

 

[HallsofIvy]

In other words, they are using the circular symmetry of the figures, integrating from 0 to $\pi/2$, rather than from 0 to $2\pi$, then multiplying by 4.