Use spherical coordinates to evaluate the following integral, ∫
∫ ∫ y2z dV, E where E...
Use spherical coordinates to evaluate the following integral, ∫
∫ ∫ y2z dV, E where E lies above the cone φ = π 4 and below the
sphere ρ = 9
Evaluate, in spherical coordinates, the triple integral of
f(ρ,θ,ϕ)=cosϕ, over the region 0≤θ≤2π, π/6≤ϕ≤π/2, 3≤ρ≤8.
integral...
Evaluate, in spherical coordinates, the triple integral of
f(ρ,θ,ϕ)=cosϕ, over the region 0≤θ≤2π, π/6≤ϕ≤π/2, 3≤ρ≤8.
integral =
Change from rectangular to spherical coordinates. (Let ρ ≥ 0, 0
≤ θ ≤ 2π, and...
Change from rectangular to spherical coordinates. (Let ρ ≥ 0, 0
≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π.)
(a) (0, −3, 0):
(ρ, θ, ϕ) = (3, −π 2 , π 2) <---- (WRONG!!!!)
(b) (−1, 1, − 2 ):
(ρ, θ, ϕ) = (2, − π 4 , π 4) <------ (WRONG!!!!)
Change from rectangular to spherical coordinates. (Let ρ ≥ 0, 0
≤ θ ≤ 2π, and...
Change from rectangular to spherical coordinates. (Let ρ ≥ 0, 0
≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π.) (a) (0, −3, 0) (b) (−1, 1, − sqrt 2 )
1) Convert the point (x,y,z)=(−2,5,3) to spherical coordinates.
Give answers as positive values, either as expressions,...
1) Convert the point (x,y,z)=(−2,5,3) to spherical coordinates.
Give answers as positive values, either as expressions, or decimals
to one decimal place.
(ρ,θ,ϕ)=
2) Convert the point (r,θ,z)=(2,2π,4) to Cartesian coordinates.
Give answers either as expressions, or decimals to at least one
decimal place.
(x,y,z)=
3) Convert the point (ρ,θ,ϕ)= (5,5π/3,3π/4) to Cartesian
coordinates. Give answers either as expressions, or decimals to at
least one decimal place.
(x,y,z) =