Use cylindrical coordinates to compute the integral of f(x, y, z) =(x^2+y^2)^.5 over the region described by x^2+y^2
Please Help!! Thanks!!! <3
Please Help!! Thanks!!! <3
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Converting to cylindrical coordinates yields
x^2 + y^2 = 4 ==> r = 2.
So, ∫∫∫ (x^2 + y^2)^(1/2) dV
= ∫(θ = 0 to 2π) ∫(r = 0 to 2) ∫(z = 0 to 2) (r^2)^(1/2) * r dz dr dθ
= ∫(θ = 0 to 2π) dθ * ∫(r = 0 to 2) r^2 dr * ∫(z = 0 to 2) dz
= 2π * (8/3) * 2
= 32π/3.
I hope this helps!
x^2 + y^2 = 4 ==> r = 2.
So, ∫∫∫ (x^2 + y^2)^(1/2) dV
= ∫(θ = 0 to 2π) ∫(r = 0 to 2) ∫(z = 0 to 2) (r^2)^(1/2) * r dz dr dθ
= ∫(θ = 0 to 2π) dθ * ∫(r = 0 to 2) r^2 dr * ∫(z = 0 to 2) dz
= 2π * (8/3) * 2
= 32π/3.
I hope this helps!