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Math Help - Volume of a solid

  1. #1
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    Volume of a solid

    Volume of a solid formed when the region bounded by the graphs y=x^3, y=0, x=1 is revolved about line x=2.
    I don't know where to start. Shell Method?
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  2. #2
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    Quote Originally Posted by JJ007 View Post
    Volume of a solid formed when the region bounded by the graphs y=x^3, y=0, x=1 is revolved about line x=2.
    I don't know where to start. Shell Method?
    shells is one possibility ...

    V = 2\pi \int_a^b r(x) \cdot h(x) \, dx

    sketch your representative rectangle in the described region

    a = 0

    b = 1

    r(x) = 2-x

    h(x) = x^3
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  3. #3
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    Got it. So for a similar one: y=x^2, y=4 revolved about the x-axis would be:
    V=2\pi\int_0^4y[\sqrt{y}-0]dy ?

    Thanks.
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  4. #4
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    Quote Originally Posted by JJ007 View Post
    Got it. So for a similar one: y=x^2, y=4 revolved about the x-axis would be:
    V=2\pi\int_0^4y[\sqrt{y}-0]dy ?

    Thanks.
    if it is only the region in quad I that is rotated, then your integral set up is correct.
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