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?

- anonymous

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- schrodinger

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- amistre64

all of them lol

- anonymous

thanks :D

- anonymous

I've tried all of them, and I still get the wrong answer

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## More answers

- anonymous

The shell method gives me -8pi, and the disk method gives me a ridiculous number

- amistre64

the question seems to be asking you to do it 4 different times...

- anonymous

Oh, my question uses the y-axis.

- anonymous

There's a list of them, and I have already done the one revolving around the x-axis

- amistre64

is this our region?

##### 1 Attachment

- amistre64

if you wanna spin it round the y axis; shell it.
2pi 6 {S} x(1/x^2) dx ; [1,3]

- anonymous

Yes...so I thought to use the shell method first....right., that's what I did, and got -8pi

- amistre64

1/x ints up to ln(x) right?
so 12pi ln(x)

- anonymous

wait---you separated the 6 from the equation, and multiplied by x instead of (x + 1) or some variation of that?

- amistre64

12pi ln(3) should be it ; since ln(1) = 0

- amistre64

constants dont get inted; they get pulled out, thats why we dont int pi and 2pi and the like

- amistre64

we dont derive constants either; so why bother inting them lol

- amistre64

sine the y axis is alreay x = 0; no need to move anything

- 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

\[2\pi \int\limits_{a}^{b}r(x)h(x)dx\]

- 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

the radius in the shell method is...? as you move from 1 to 3?

- amistre64

what are we spinning around?

- anonymous

the y-axis

- amistre64

does the y axis the same as the x=0 axis?

- anonymous

?

- amistre64

is the y axis that same as the x=0 line?

- anonymous

y = 0 and x = 0 look the same....oh, okay

- amistre64

since y axis IS x=0; then what do we move to get this to x=0? nothing right?

- amistre64

so r(x) = x ; h(x) = 6/x^2
r(x)h(x) = 6/x from 1 to 3

- amistre64

12pi/x ints to 12pi ln(x) which means the the answer is:
12pi ln(3)

- anonymous

the answer is right! i get it----what your second to last post was. This makes sense now.

- amistre64

:)

- anonymous

Thanks! See yah next time

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