How to integrate this function

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athrun200
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Homework Statement



Printed problem 3: Find the area of the paraboloid x^2 + y^2 = z inside the cylinder x^2 + y^2 = 9.


Homework Equations





The Attempt at a Solution


Handwritten calculus working: a small circle of radius 3 in the xy-plane, with the gradient of phi = 4 - x^2 - y^2 and the surface area integral A = 4 times the double integral of sqrt(4x^2 + 4y^2 + 1) dy dx over the quarter disc.


How to integrate this function?
 
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  • Printed problem 3: Find the area of the paraboloid x^2 + y^2 = z inside the cylinder x^2 + y^2 = 9.
    1.jpg
    5.5 KB · Views: 479
  • Handwritten derivation of a surface area integral: a circle of radius 3 in the xy-plane, gradient of phi = 2 - x^2 - y^2, sec gamma = sqrt(4x^2+4y^2+1), leading to A = 4 times the double integral from x = 0 to 3 and y = 0 to sqrt(9 - x^2) of sqrt(4x^2+4y^2+1) dy dx.
    2.jpg
    26.5 KB · Views: 465
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Discussion

You might want to convert your integral to polar coordinates.
 

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