anonymous
  • anonymous
Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y = 6/x^2 y = 0 x = 1 x = 3 What method should I use?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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amistre64
  • amistre64
all of them lol
anonymous
  • anonymous
thanks :D
anonymous
  • anonymous
I've tried all of them, and I still get the wrong answer

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More answers

anonymous
  • anonymous
The shell method gives me -8pi, and the disk method gives me a ridiculous number
amistre64
  • amistre64
the question seems to be asking you to do it 4 different times...
anonymous
  • anonymous
Oh, my question uses the y-axis.
anonymous
  • anonymous
There's a list of them, and I have already done the one revolving around the x-axis
amistre64
  • amistre64
is this our region?
1 Attachment
amistre64
  • amistre64
if you wanna spin it round the y axis; shell it. 2pi 6 {S} x(1/x^2) dx ; [1,3]
anonymous
  • anonymous
Yes...so I thought to use the shell method first....right., that's what I did, and got -8pi
amistre64
  • amistre64
1/x ints up to ln(x) right? so 12pi ln(x)
anonymous
  • anonymous
wait---you separated the 6 from the equation, and multiplied by x instead of (x + 1) or some variation of that?
amistre64
  • amistre64
12pi ln(3) should be it ; since ln(1) = 0
amistre64
  • amistre64
constants dont get inted; they get pulled out, thats why we dont int pi and 2pi and the like
amistre64
  • amistre64
we dont derive constants either; so why bother inting them lol
amistre64
  • amistre64
sine the y axis is alreay x = 0; no need to move anything
anonymous
  • anonymous
so we don't add or subtract anything from the r(x) factor in [\int\limits_{a}^{b}r(x)h(x)dx\] if y = 0?
anonymous
  • anonymous
\[2\pi \int\limits_{a}^{b}r(x)h(x)dx\]
amistre64
  • amistre64
nope; the radius in the shell method is as you move from 1 to 3 in this and the height is 6/x^2
anonymous
  • anonymous
the radius in the shell method is...? as you move from 1 to 3?
amistre64
  • amistre64
what are we spinning around?
anonymous
  • anonymous
the y-axis
amistre64
  • amistre64
does the y axis the same as the x=0 axis?
anonymous
  • anonymous
?
amistre64
  • amistre64
is the y axis that same as the x=0 line?
anonymous
  • anonymous
y = 0 and x = 0 look the same....oh, okay
amistre64
  • amistre64
since y axis IS x=0; then what do we move to get this to x=0? nothing right?
amistre64
  • amistre64
so r(x) = x ; h(x) = 6/x^2 r(x)h(x) = 6/x from 1 to 3
amistre64
  • amistre64
12pi/x ints to 12pi ln(x) which means the the answer is: 12pi ln(3)
anonymous
  • anonymous
the answer is right! i get it----what your second to last post was. This makes sense now.
amistre64
  • amistre64
:)
anonymous
  • anonymous
Thanks! See yah next time

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