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Volumes of Revolution watch

1. I have this question which is rather interesting and quite hard IMO.

I have to find the volumes of revolution generated by the regions A and B when they are each rotated about: the x axis and the y axis

If the equation was from a to b,then it means I need to find the volume of revolution for:

• x = a to b, rotated around the x axis, which would be:
• y = a to b, roated around the y axis, which would be:

are those right?

I also have to find this though and this is what I need help with:

• x = a to b, rotated around the y axis
• y = a to b, roated around the x axis

How would you find those?
2. For the last two, if you have the y co-ordinates and need x co-ordinates, just plug the y co-ordinates into the equation to find the relevant x's. (or vice versa)
3. (Original post by TomLeigh)
For the last two, if you need y co-ordinates and need x co-ordinates, just plug the y co-ordinates into the equation to find the relevant x's.
I have the coordinates, I have to rotate it around the opposite axis. For example, if the function was , most questions would ask for the volume of revolution from to , rotated around the x axis.

My question is asking the exact same thing, except rotated around the y axis
4. Yes so find out what y is at x=1 and x=3 (y=1 and y=9) and use those y co-ordinates to rotate around y.
5. I can see the sense in that, and I don't want to undermine your math skills, but are you sure that is right?

Because my book doesn't have answers so by doing this I wouldn't know if I get the right answer
6. Ah well I could easily be wrong don't worry. I've only just done this chapter but I just used my common sense mixed with the rules we learned in class. If you think about 2 points on an axis say, 3 and 2, with th graph say y=x^2, then you're not going to use the points (3,0) (2,0) as these would make an area of 0, and the only co-ordinates that you can use with these are the x,y co-ordinates, being (3,9) (2,4) If you get me
7. Anyone else?
8. you have a formula for y in terms of x. Presuming you've done integration by substitution you should be able to make this work by making a substitution for y or x depending on the situation. There may well be a quicker way that someone knows of but I believe this should lead you to the answer.
9. (Original post by JoMo1)
you have a formula for y in terms of x. Presuming you've done integration by substitution you should be able to make this work by making a substitution for y or x depending on the situation. There may well be a quicker way that someone knows of but I believe this should lead you to the answer.

I dont understand
10. For rotating around the y-axis, it would be

not

.
11. (Original post by Rainfaery)
For rotating around the y-axis, it would be

not

.
thats what i thought but if then

= =

hence,

12. (Original post by G O D I V A)
thats what i thought but if then

= =

hence,

No, when you have a power to a power, they are multiplied together. If you square that, you just get y, because (1/2)^2 is just (2/2), which is one. This is just a basic property of indices.
13. Oh thanks for that.

I still have to find though,

* x = a to b, rotated around the y axis
* y = a to b, roated around the x axis

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