Integral of $f(x, y, z)= x^2 +z $ over the surface area of a cone

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For $C subset R^3$ a circular cone, with a base area of a circle in the $(x,y)$ plane with the center $(0,0)$ and radius $r$. The tip of the cone is located in $(0,0,h)$. I should calculate the integral of the function beginequation
f(x,y,z)= x^2 + z
endequation
over the surface area of $C$.



I drew the cone and got from the geometry the following:
beginequation
z= cot(phi)cdot r
endequation
and beginequation
z^2=dfrach^2(x^2+y^2)r^2
endequation
Can anyone tell me what to do next? The boundary seems difficult for me to use too.




integration multivariable-calculus surface-integrals multiple-integral




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    For $C subset R^3$ a circular cone, with a base area of a circle in the $(x,y)$ plane with the center $(0,0)$ and radius $r$. The tip of the cone is located in $(0,0,h)$. I should calculate the integral of the function beginequation
    f(x,y,z)= x^2 + z
    endequation
    over the surface area of $C$.



    I drew the cone and got from the geometry the following:
    beginequation
    z= cot(phi)cdot r
    endequation
    and beginequation
    z^2=dfrach^2(x^2+y^2)r^2
    endequation
    Can anyone tell me what to do next? The boundary seems difficult for me to use too.




    integration multivariable-calculus surface-integrals multiple-integral




    share|cite|improve this question























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      For $C subset R^3$ a circular cone, with a base area of a circle in the $(x,y)$ plane with the center $(0,0)$ and radius $r$. The tip of the cone is located in $(0,0,h)$. I should calculate the integral of the function beginequation
      f(x,y,z)= x^2 + z
      endequation
      over the surface area of $C$.



      I drew the cone and got from the geometry the following:
      beginequation
      z= cot(phi)cdot r
      endequation
      and beginequation
      z^2=dfrach^2(x^2+y^2)r^2
      endequation
      Can anyone tell me what to do next? The boundary seems difficult for me to use too.




      integration multivariable-calculus surface-integrals multiple-integral




      share|cite|improve this question













      For $C subset R^3$ a circular cone, with a base area of a circle in the $(x,y)$ plane with the center $(0,0)$ and radius $r$. The tip of the cone is located in $(0,0,h)$. I should calculate the integral of the function beginequation
      f(x,y,z)= x^2 + z
      endequation
      over the surface area of $C$.



      I drew the cone and got from the geometry the following:
      beginequation
      z= cot(phi)cdot r
      endequation
      and beginequation
      z^2=dfrach^2(x^2+y^2)r^2
      endequation
      Can anyone tell me what to do next? The boundary seems difficult for me to use too.





      integration multivariable-calculus surface-integrals multiple-integral





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Aug 6 at 11:04









      Sou

      2,7062820




      2,7062820









      asked Aug 6 at 10:58









      Mohamed Mossad

      103




      103

























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