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Math Help - Computing surface area with double integrals help

  1. #1
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    Computing surface area with double integrals help

    Compute the surface area of the part of the cylinder x^2 + y^2 = 1, z>=0, between the planes y=0 and z=y+1

    And one more!: Find the area of the triangle with vertices (1,2,0), (3,0,7), and (-1,0,0) using a surface integral. Check your answer using the cross product


    I have no idea how to do these.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    In the first case make sure you are familiar with the surface area formula for a function z = f(x,y)

    In your first problem use the analagous formula where x = f(y,z)

    In particular:

    x= (1-y^2)^(1/2)

    dS = [(dx/dy)^2 + (dx/dz)^2 +1]^(1/2) dzdy

    By Symmetry you can do half and double it

    The region of integration is the trapezoidal region in the yz plane

    where z varies from 0 to y + 1 and y varies from 0 to 1.

    In the second problem you should know how to find the equation of a plane using 3 points. You probably did this much earlier in the semester so if you forgot look it up.

    Once you have z = f(x,y) then it is fairly easy to see the region of integration in the xy plane is the triangular region with vertices

    (-1,0), (1,2), and (3,0)
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