Volumes Q (2 Viewers)

[girrawhat]

Can someone pls help me with another question. I'm still struggling with volumes. It is

Find volume bounded between y=x, y=-(x^1/2), and x=4.
part1. About line x=6
part2. about line y=6

Could u please state what method (shell or washer) u will use for both and a brief description why when explaining. I for some reason keep choosing the longer method.

I also get different answers when using both methods.

 

[girrawhat]

Also, from a past paper, I found the question

Find the volume generated by rotating the region bounded by y=x/2 and y=x^1/2 about the x-axis. Unfortunately I dont have solutions and I have no clue what I am doing. Could anybody pls help :/

 

[Carrotsticks]

Do you know the basics ie: constructing discs/shells etc?

 

[girrawhat]

I think I know basics okay now but i cannot recognise when it would be better to use a particular method. I blindly choose a particular method and I get an ugly expression but when I try another way I get a better expression. But by then, it would be too late. How do u tell straight from seeing the question what method to use. I think i take too long for volume questions

 

[Carrotsticks]

I think I know basics okay now but i cannot recognise when it would be better to use a particular method. I blindly choose a particular method and I get an ugly expression but when I try another way I get a better expression. But by then, it would be too late. How do u tell straight from seeing the question what method to use. I think i take too long for volume questions

The best way to know is to look at your function and think 'would it be easier to integrate this with respect to x, or y?

Reason is because suppose rotation is around the Y axis (or parallel to it). Using Shells would give you a delta x (so integration is with respect to x) whereas Discs would give you a delta y (so integration is with respect to y) etc.

So for your example there, it would probably be easier to integrate with respect to x (since everything is already in terms of x) so best to use Shells.

 

[girrawhat]

Could u think of an example where it would not be better to use shells cos i find that i am trying to use shells for everything.

 

[girrawhat]

Reason is because suppose rotation is around the Y axis (or parallel to it). Using Shells would give you a delta x (so integration is with respect to x) whereas Discs would give you a delta y (so integration is with respect to y) etc.

Wouldn't using shells give u a delta y

 

[Carrotsticks]

Wouldn't using shells give u a delta y

Yep as I was reading my response, I saw that I had typed X instead of Y and edited it about 30 seconds before you posted this =)

Also, consider the curves y=-0.5x and y=x(x^2-1). Suppose we want to get the area bounded by the two curves in the 4th Quadrant, then rotate it sound the x axis.

Shells: We would have delta Y, meaning we have to integrate with respect to Y, meaning we need to make X the subject. This is a pain since we have a cubic (even quadratics are pretty bad as well)

Slicing: Everything is already set out, so you can jump directly into delicious integration.

 

[girrawhat]

Is the answer 27pi / 40(root2) units cubed?

 

[girrawhat]

Thanks man, that was very well explained

 

[Johnstan]

hey OP do u go to girra?
also when r ur trials?
all the best man.

 

[girrawhat]

I do indeed go to girra. Trial period has just started. I have my first exam on tuesday, extension 2 is on Wednesday. Thanks, I need all the luck I can get. U have ur trials yet?

 

[Carrotsticks]

Is the answer 27pi / 40(root2) units cubed?

Haha I have no idea! I just made that question up.

Would you like me to do it for you?

 

[girrawhat]

Yes pls

 

[Johnstan]

I do indeed go to girra. Trial period has just started. I have my first exam on tuesday, extension 2 is on Wednesday. Thanks, I need all the luck I can get. U have ur trials yet?

ok awesome!
u must be super smart then
and nah havent started yet... my 4unit is tomorrow and 3unit is friday.. then im done biatches!

 

[girrawhat]

ok awesome!
u must be super smart then
and nah havent started yet... my 4unit is tomorrow and 3unit is friday.. then im done biatches!

Haha, I'm not particularly smart or anything. If u dont mind me asking, what school do u go to? If I can survive first week of trials I will be relieved. English on Tuesday, Ext 2 on Wednesday and English paper 2 on Thursday. At the end of next week, I am done.

 

[Carrotsticks]

Just did it quickly and got pi/sqrt(2) * 29/140.

Could somebody else please confirm? I have other things to do atm.

 

[girrawhat]

which radius we subtract from the other radius? is it pi[(x^2-1)^2 -(-0.5x)^2]delta x or pi[(-0.5x)^2 - (x^2-1)^2]delta x

 

[Carrotsticks]

But the curve isn't y=x^2-1, it is y=x^3-x or y=x(x^2-1).

 

[kingkong123]

Just did it quickly and got pi/sqrt(2) * 29/140.

Could somebody else please confirm? I have other things to do atm.

i got <a href="http://www.codecogs.com/eqnedit.php?latex=\frac{3\pi\sqrt2}{140}$ units^{3}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\frac{3\pi\sqrt2}{140}$ units^{3}" title="\frac{3\pi\sqrt2}{140}$ units^{3}" /></a>