anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
Do you have a second bound, or is x=6 the second one?
anonymous
  • anonymous
thats all we were given for the bounded region
anonymous
  • anonymous
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

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anonymous
  • anonymous
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.
anonymous
  • anonymous
I have a class soon, so I hope this is enough to help you.
anonymous
  • anonymous
You would be integrating from x = 1 to 6.
anonymous
  • anonymous
thanks but how to you determine your intervals?
anonymous
  • anonymous
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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