Use Polar coordinates to find volume of the solid under the paraboloid z=x^2+y^2 and above the disk x^2+y^2 May 1, 2021 by thanh

NetherCraft 0

I am lost completely on how to work this problem out.

Please help!


2 Answers

  • In polar/cylindrical coordinates, x^2 + y^2 = r^2.

    In particular, x^2 + y^2 <= 9 ==> r^2 <= 9 ==> r <= 3.

    Since this is a disc at the origin, θ is in [0, 2π].

    V = ∫∫ (x^2 + y^2) dA

    = ∫(θ = 0 to 2π) ∫(r = 0 to 3) (r^2) (r dr dθ).

    Evaluating this yields

    (∫(θ = 0 to 2π) dθ) * (∫(r = 0 to 3) r^3 dr)

    = 2π * r^4/4 {for r = 0 to 3}

    = 81π/2.

    I hope this helps!

  • it style of sounds such as you’re meant to be doing a triple needed (which simplifies to a double needed) you combine from z= 2+x^2+(y-2)^2 to z=a million interior the z direction. This in simple terms components the function 2+x^2+(y-2)^2 – a million = a million+x^2+(y-2)^2 then you definately evaluate the double needed of a million+x^2+(y-2)^2 as substantially used. want this facilitates and good fulfillment.

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