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Friday, May 29, 2020

Integration in the spherical coordinate

d3r=r2drsinθdθdϕ
Since dcos(θ)=sin(θ)dθ,
d3r=r2drdcos(θ)dϕ,
let μ=cos(θ),
π0d3r=π0r2drdcos(θ)dϕ=cos(2π)cos(0)r2drdμdϕ=cos(2π)cos(0)r2drdμdϕ=cos(0)cos(2π)r2drdμdϕ=11r2drdμdϕ

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