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anonymous

  • 5 years ago

i need help with rotations? how do you determine what your equation to integrate is and what your boundaries are (if left out) and solve the problem? For example: Determine the volume of the solid obtained by rotating the region bounded by 2*(square root of x-1) and about the line x=6.

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  1. anonymous
    • 5 years ago
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    Do you have a second bound, or is x=6 the second one?

  2. anonymous
    • 5 years ago
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    thats all we were given for the bounded region

  3. anonymous
    • 5 years ago
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    If I understand the question correctly, the method of cylindrical shells is the easiest way to go. You have to set up an elemental cylindrical shell volume and integrate each shell. The volume of a shell is: dV = 2pi*radius*height*(elemental thickness) dV = 2pi*(6-x)*y*dx dV = 2pi*(6-x)*2sqrt(x-1)dx = 4pi(6-x)sqrt(x-1)dx

  4. anonymous
    • 5 years ago
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    If you expand: dV = 4pi[6sqrt(x-1)-xsqrt(x-1)]dx and use the substitution u^2=x-1 in the second one, you should be able to pump it out.

  5. anonymous
    • 5 years ago
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    I have a class soon, so I hope this is enough to help you.

  6. anonymous
    • 5 years ago
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    You would be integrating from x = 1 to 6.

  7. anonymous
    • 5 years ago
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    thanks but how to you determine your intervals?

  8. anonymous
    • 5 years ago
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    Plot the function 2sqrt(x-1) from x=1 to 6. You can't go below 1 since the radical won't be real anymore, and you can't go above 6 because it's the axis of rotation.

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