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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 x1) and about the line x=6.
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 x1) and about the line x=6.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you have a second bound, or is x=6 the second one?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats all we were given for the bounded region

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If 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*(6x)*y*dx dV = 2pi*(6x)*2sqrt(x1)dx = 4pi(6x)sqrt(x1)dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If you expand: dV = 4pi[6sqrt(x1)xsqrt(x1)]dx and use the substitution u^2=x1 in the second one, you should be able to pump it out.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I have a class soon, so I hope this is enough to help you.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You would be integrating from x = 1 to 6.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks but how to you determine your intervals?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Plot the function 2sqrt(x1) 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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