Surface area with double integrals

Lessons

• Introduction
  Surface Area with Double Integrals Overview:
  a)

  • Surface Area with a function with Region $D$
  • Partial Derivatives
  
  
  b)

  • Find the Region $D$
  • Find the partial derivatives $f_x$ & $f_y$
  • Calculate the Double Integral
  
  

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• 1.
  Finding the Surface Area with Double Integrals
  Determine the surface area of the surface $\, x + 2y + 2z = 4$ that is in the 1^st octant.

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• 2.
  Determine the surface area of the surface $\, z = 2 - x^{2} - y^{2}$ that is above $z = 1 + x^{2} + y^{2}$ with $x \geq 0$ and $y \geq 0$.

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• 3.
  Determine the surface area of the surface $\, y = 3x^{2} + 3z^{2} - 4$ that is inside the cylinder $x^{2} + z^{2} =1$.

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