anonymous
  • anonymous
Find the volume generated by revolving about the x-axis the area bounded by xy = 9, the x-axis and lines x = 3 and x=9
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
|dw:1324412465826:dw|
amistre64
  • amistre64
something similar to this right?
anonymous
  • anonymous
Yess

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amistre64
  • amistre64
then we can integrate, or sum up the areas of circles, generated by the function from 3 to 9 i believe
anonymous
  • anonymous
May I please see a full work out please?
anonymous
  • anonymous
@ amistre64 Alright
amistre64
  • amistre64
\[\sum_{3}^{4}\pi[f(x)]^2\ \Delta x\] \[\pi \int_{3}^{9}(\frac{9}{x})^2dx\]
amistre64
  • amistre64
|dw:1324412686951:dw|
amistre64
  • amistre64
if we take any arbitrary circle created by spinning this about the x axis; we get an area of: pi (y)^2 pi (9/x)^2 the volume generated is then adding up all the circles made from x=3 to x=9
TuringTest
  • TuringTest
are you still stuck? can you not integrate\[\pi\int_{3}^{9}\frac{9^2}{x^2}dx\]? or are you having another problem?
anonymous
  • anonymous
@ amistre64 Alright
anonymous
  • anonymous
is it 18pi?
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=integrate+pi*%289%2Fx%29%5E2+from+3+to+9 18pi looks good to me

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