In the spherical coordinates, the triple integral of f(rho,θ,ϕ)=cosϕ, over the region 0≤θ≤2π, 0≤ϕ≤π/4, 3≤rho≤4 is .
Spherical coordinates of the gadget denoted as (r, θ, Φ) is the coordinate machine specifically used in three-dimensional systems. In 3 dimensional area, the round coordinate gadget is used for finding the surface region. those coordinates specify 3 numbers: radial distance, polar angles, and azimuthal perspective.
To convert a factor from spherical coordinates to Cartesian coordinates, use equations x=ρsinφcosθ,y=ρsinφsinθ, and z=ρcosφ. To transform a factor from Cartesian coordinates to spherical coordinates, use equations ρ2=x2+y2+z2,tanθ=yx, and φ=arccos(z√x2+y2+z2).
Consider the function:
f(0,0,0)=cos
35057
Spherical Coordinates:
x=psin cos
y=psin sine
z = p cos
DV = p² sin dpdøde
1=[[[psin p cos dpdøde
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= "deƒân (20)deſp°dp
-(2x) (1-1) (343-27)
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pm (316
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