anonymous
  • anonymous
Find volume of the solid generated by rotating the plane region bounded by x2−4x+2=y and y=2 about the line y=2. I'm having troubles finding the radius so i can do the question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
that' x^2 - 4x + 2 = y
anonymous
  • anonymous
The radius is the whole equation integrated
anonymous
  • anonymous
|dw:1332738162228:dw| look at the radius with respect to the representative rectangle. axis or revolution is y = 2. The height of the function is given by y = x^2 - 4x + 2. So, what is R = ?

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anonymous
  • anonymous
but what about the part below the x axis? that's what's stumping me
anonymous
  • anonymous
let's try it this way...|dw:1332738479158:dw| look at A, look at B. so R = A - B....?
anonymous
  • anonymous
it doesn't matter...
anonymous
  • anonymous
okay, what confused me was when i looked at the solution it said "Thinking of x as the vertical axis, we set outer function o(x)=x^2−4x+2, inner function i(x)=2 and L=2. "
anonymous
  • anonymous
in this case, you don't have an inner function and outer function because the region is on th axis of revolution -- no hole. no inner function. just an outside function.
anonymous
  • anonymous
i guess you could also think of your inside function as 0.
anonymous
  • anonymous
|dw:1332738841384:dw|
anonymous
  • anonymous
is it the other way around; x^2-4x+2 -2 ?
anonymous
  • anonymous
to get your radius, R = A - B = 2 - y = 2 - [x^2 -4x + 2]
anonymous
  • anonymous
will that give me the same answer if i went R = B-A ? the solution manual has it that way.
anonymous
  • anonymous
wow, i was typing your answer the same time you were typing out the question :)
anonymous
  • anonymous
idk how your solution book set it up but the answers should be the same. there are diferent methods of doing this but no matter what, the volume should be the same.
anonymous
  • anonymous
according to the way we did it here, our volume is...
anonymous
  • anonymous
512pi/15
anonymous
  • anonymous
what's the answer on your solution book?
anonymous
  • anonymous
it's the same. i don't understand the method the book uses but i like yours way better. thanks!
anonymous
  • anonymous
yw

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