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Paul's Online Notes
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Home / Calculus II / Applications of Integrals / Surface Area
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Section 8.2 : Surface Area

  1. Set up, but do not evaluate, an integral for the surface area of the object obtained by rotating x=y+5 , 5x3 about the y-axis using,
    1. ds=1+[dydx]2dx
    2. ds=1+[dxdy]2dy
    Solution
  2. Set up, but do not evaluate, an integral for the surface area of the object obtained by rotating y=sin(2x) , 0xπ8 about the x-axis using,
    1. ds=1+[dydx]2dx
    2. ds=1+[dxdy]2dy
    Solution
  3. Set up, but do not evaluate, an integral for the surface area of the object obtained by rotating y=x3+4 , 1x5 about the given axis. You can use either ds.
    1. the x-axis
    2. the y-axis
    Solution
  4. Find the surface area of the object obtained by rotating y=4+3x2 , 1x2 about the y-axis. Solution
  5. Find the surface area of the object obtained by rotating y=sin(2x) , 0xπ8 about the x-axis. Solution