Disk/Washer Method

[ad1]

If anyone could help me out with this problem it would be so great, been stuck with it for a week+ and just cant figure out where I go wrong.

Here is what i have;

Rotates around the Y-axis. Lower limit 0, upper limit 8.

I calculate X^2 in order to be able to replace it later:

with the Disk/Washer method I get:

Now the problem is that I cant get the same answer with the shell method. As I said i've been at it for a long time and if anyone could help me out that would be great <3

 

[mmm4444bot]

The image tags are for images only; you can't attach a website result as an image.

:idea: There is no need to link images of such simple equations; simply type them.

8 = k*6^2 - 3

x^2 = 36/11*(Y + 3)

 

[Quaid]

Here is what i have;

8 = k*6^2 - 3

Rotates around the Y-axis. Lower limit 0, upper limit 8.

Is that equation a typo?

What exactly is rotating around the Y-axis? (It's not that equation.)

Also, you have not defined symbol k.

I calculate X^2 in order to be able to replace it later:

X^2 = 36/11 (Y + 3)

with the Disk/Washer method I get:

Now the problem is that I cant get the same answer with the shell method.

(I changed your symbol x to X. Once you start using symbols X,Y don't switch or interchange them with symbols x,y)


What is a.e^3 supposed to be, in your result above?

If the problem is with your shell method, then you need to show your work with the shell method.

 

[ad1]

Is that equation a typo?

What exactly is rotating around the Y-axis? (It's not that equation.)

Also, you have not defined symbol k.




(I changed your symbol x to X. Once you start using symbols X,Y don't switch or interchange them with symbols x,y)


What is a.e^3 supposed to be, in your result above?

If the problem is with your shell method, then you need to show your work with the shell method.

Sry guys, first time posting

Anyways;

8=k*(6^2)-3 ---> 11=36k ---> k=11/36

for the substitution:

Y=(11/36)k-3 ---> X^2= (36/11)*(Y+3).

I showed my work for the washer method so here is the shell method, where I think I go wrong.

I can not get this to equal 575cm^3. I hope there aren't any more uncertainties.

edit: Again with the links -.-, anyone know a better way to share equations on here?

I used:

http://www.codecogs.com/latex/eqneditor.phphttp://www.codecogs.com/latex/eqneditor.php

Input:

V=2\pi \int _{0}^{6}y*xdx = 2\pi \int _{0}^{6}\left ( \frac{36}{11}*\left ( x^{2}-3 \right ) x\right )dx = 2\pi \left [ \frac{36}{11}\left ( \frac{x^{4}}{4} -\frac{3x^{^{2}}}{2}\right ) \right ]_{0}^{6}

Sry again for being so **** new

 

[Quaid]

What exactly is rotating around the Y-axis?