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?

Question

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?

amistre64 · Answer

all of them lol

anonymous · Answer

thanks :D

anonymous · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

Oh, my question uses the y-axis.

anonymous · Answer

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

amistre64 · Answer

is this our region?

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

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 · Answer

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

amistre64 · Answer

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 · Answer

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

amistre64 · Answer

what are we spinning around?

anonymous · Answer

the y-axis

amistre64 · Answer

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

anonymous · Answer

?

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

:)

anonymous · Answer

Thanks! See yah next time