## anonymous 5 years ago 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?

1. amistre64

all of them lol

2. anonymous

thanks :D

3. anonymous

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

4. anonymous

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

5. amistre64

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

6. anonymous

Oh, my question uses the y-axis.

7. anonymous

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

8. amistre64

is this our region?

9. amistre64

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

10. anonymous

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

11. amistre64

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

12. anonymous

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

13. amistre64

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

14. amistre64

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

15. amistre64

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

16. amistre64

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

17. 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?

18. anonymous

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

19. 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

20. anonymous

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

21. amistre64

what are we spinning around?

22. anonymous

the y-axis

23. amistre64

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

24. anonymous

?

25. amistre64

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

26. anonymous

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

27. amistre64

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

28. amistre64

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

29. amistre64

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

30. anonymous

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

31. amistre64

:)

32. anonymous

Thanks! See yah next time