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Shell Method Setup

  • Thread starter icesalmon
  • Start date
  • #1
244
6

Homework Statement


use the shell method to find the volume of the solid given by y = 4x - x2 y = x2, about the line x = 4

The Attempt at a Solution


I have to find a height and a radius multiply them together and integrate them over some bounded region, fair enough. My functions intersect at x = 2 and x = 0, my bounds have been set. I have to find my height, which I believe to be "x", and my radius. I believe that to be my top function, 4x - x2 - my bottom function, x2 so I multiply them within my integrand to get 4x2 - 2x3 after integrating I get 4x3/3 - x4 / 2. Evaluating this expression at x = 2 I get 32/3 - 24/3 multiplied by 2pi to get 16pi/3. My book tells me it is 16pi so I went back and looked at this a few times and did the calculation over and i'm getting the same answer and i'm not sure where i'm getting this wrong with my geometry.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
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Homework Statement


use the shell method to find the volume of the solid given by y = 4x - x2 y = x2, about the line x = 4

The Attempt at a Solution


I have to find a height and a radius multiply them together and integrate them over some bounded region, fair enough. My functions intersect at x = 2 and x = 0, my bounds have been set. I have to find my height, which I believe to be "x", and my radius. I believe that to be my top function, 4x - x2 - my bottom function, x2 so I multiply them within my integrand to get 4x2 - 2x3 after integrating I get 4x3/3 - x4 / 2. Evaluating this expression at x = 2 I get 32/3 - 24/3 multiplied by 2pi to get 16pi/3. My book tells me it is 16pi so I went back and looked at this a few times and did the calculation over and i'm getting the same answer and i'm not sure where i'm getting this wrong with my geometry.
Your height is 4x-2x^2. Your radius isn't x. You are rotating around x=4. What is it?
 
  • #3
244
6
*sigh* 4-x
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
619

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