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Surface area with double integrals
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Surface area with double integrals
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Surface Area with Double Integrals
Surface Area with Double Integrals
Suppose we want to find the surface area given by the function f(x,y) from the region D. Then the surface area can be calculated using the following:
S=∫∫D[fx]2+[fy]2+1dA
- IntroductionSurface 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 fx & fy
- Calculate the Double Integral
- 1.Finding the Surface Area with Double Integrals
Determine the surface area of the surface x+2y+2z=4 that is in the 1st octant. - 2.Determine the surface area of the surface z=2−x2−y2 that is above z=1+x2+y2 with x≥0 and y≥0.
- 3.Determine the surface area of the surface y=3x2+3z2−4 that is inside the cylinder x2+z2=1.
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6.
Multiple Integral Applications
6.1
Change in variables
6.2
Moment and center of mass
6.3
Surface area with double integrals