Surface area with double integrals

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Surface Area with Double Integrals Overview:
- Surface Area with a function with Region $D$
- Partial Derivatives
- Find the Region $D$
- Find the partial derivatives $f_x$ & $f_y$
- Calculate the Double Integral

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Finding the Surface Area with Double Integrals
Determine the surface area of the surface $\, x + 2y + 2z = 4$ $x + 2 y + 2 z = 4$ that is in the 1^st octant.
Determine the surface area of the surface $\, z = 2 - x^{2} - y^{2}$ $z = 2 - x^{2} - y^{2}$ that is above $z = 1 + x^{2} + y^{2}$ $z = 1 + x^{2} + y^{2}$ with $x \geq 0$ $x \geq 0$ and $y \geq 0$ $y \geq 0$ .
Determine the surface area of the surface $\, y = 3x^{2} + 3z^{2} - 4$ $y = 3 x^{2} + 3 z^{2} - 4$ that is inside the cylinder $x^{2} + z^{2} =1$ $x^{2} + z^{2} = 1$ .