Question

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 =

Answer #1

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 0 ≤ ϕ ≤ π.) (a) (0, −3, 0) (b) (−1, 1, − sqrt 2 )

use spherical coordinates to calculate the triple integral of
?(?, ?, ?)=?2+?2 over the region ?≤8
∫∫∫?(?^2+?^2) ??

Use spherical coordinates to calculate the triple integral
of
?(?,?,?)=1/(?^2+?^2+?^2)
over the region 6 ≤ ?^2+?^2+?^2 ≤ 25.
(Use symbolic notation and fractions where needed.)

Use spherical coordinates to calculate the triple integral of
?(?, ?, ?)=?f(x, y, z)=y over the region ?^2+?^2+?^2≤10,
∫∫∫?? ??=

Use spherical coordinates.
Evaluate
xyz
dV
E
,
where E lies between the spheres ρ = 2 and
ρ = 5 and above the cone ϕ = π/3.

Evaluate the integral.
π/2
sin5(θ) cos5(θ) dθ
0

Use spherical coordinates. y^2z^2dV, where E lies below the cone
ϕ = π/3 and above the sphere ρ = 1.

a.
r=3 - 3cos(Θ), enter value for r on a table
when;
Θ=0, (π/3),(π/2),(2π/3),π,(4π/3),(3π/2),(5π/3) & 2π
b. plot points from a, sketch graph
c. use calculus to find slope at (π/2),(2π/3),(5π/3)
& 2π
d. find EXACT area inside the curve in 1st
quadrant

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

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 4 minutes ago

asked 4 minutes ago

asked 34 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago