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Math Help - Calculating the Volume of a Solid of Revolution

  1. #1
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    Calculating the Volume of a Solid of Revolution

    Hello,

    I've been trying to calculate the volume of a solid of revolution. The 2D graph of it is the region bounded by y=x^3, y= 4+2x, and the y axis. This is rotated around the y axis. I tried both the washer and cylinder methods and each gives a different answer. Which one is the real volume, and where did I go wrong?

    Here's a graph of the problem and my results for each method:
    Calculating the Volume of a Solid of Revolution-problem.png

    Thanks!
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  2. #2
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    your method using cylindrical shells is correct.

    you have to use disks from y = 0 to y = 4 and the washers from y = 4 to y = 8 ... i.e. , two integral expressions
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  3. #3
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    Thank you so much! That work perfectly.
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