Express the the average distance from a point in a ball of radius 4 to its center as a triple integral.
NOTE: When typing your answers use "rh" for rho,rho, "ph" for ϕϕ, and "th" forθθ.
Average Distance = ∫θ2θ1∫ϕ2ϕ1∫rho2rho1drho dϕ dθrho1=rho2=ϕ1=ϕ2=θ1=θ2=∫θ1θ2∫ϕ1ϕ2∫rho1rho2drho dϕ dθrho1=rho2=ϕ1=ϕ2=θ1=θ2=
Evaluate the integral Average Distance =
Sphere:
A sphere is a three-dimensional figure. Volume of sphere is V=43πr3V=43πr3 where rr denotes the radius of the sphere.
In ∫∫∫f(x,y,z)dxdydz∫∫∫f(x,y,z)dxdydz, ∫∫∫∫∫∫ denotes triple integral, x,y,zx,y,z are variables of integration and f(x,y,z)f(x,y,z) is the integrand.