Difficulties with my assignment. Need help if anyone is up to it.

[Keba]

[SOLVED] Difficulties with my assignment. Need help if anyone is up to it.

Homework Statement

Hello.
I need to rewite the formula B so that it will become formula A, step by step. I need to explain what I do every step of the way and write all the middle-calculations also. That is, so that I can get the statement to find the Volume of a frustum cone, using the height and the two radius' of the frustum cone.

Homework Equations

http://img116.imageshack.us/img116/6908/coneuh4.jpg
Here you can see A, B, and C, and the graph I used to make C

The Attempt at a Solution

I have tried to write the correct expression for V by using the height h, the long 'radius' R, and the short 'radius' r, and writing that as a linear function. Now I need to come from C to A, but I am not aware of how I can do that. I have made a couple of attempts at using the rules for differencial and integral calculation, but with no luck. I just can't seem to get it right.
Can, and will anyone help me with this problem? (sorry for my bad english, it is not my main language)

Keba

 

[dynamicsolo]

It will probably make your life easier to start with the algebra. What do you get if you multiply out the binomial in your formula C?

(Where we are headed is to have an integrand which is a polynomial with constant coefficients -- R, r, and h -- which you can then integrate term by term.)

 

[Keba]

Well, after playing with it for a while, and integrating, I got this, but for some reason I can't seem to verify if that is correct.
http://img403.imageshack.us/img403/2056/cone1fw2.jpg
in the first one, i inserted h on the space of x, and on the second, 0 on the space of x. But I'm really not sure if that is correct, or if I should start over.
However, this is not similar to A, and I therefore need to make it smaller, if possible.

 

[dynamicsolo]

Well, after playing with it for a while, and integrating, I got this, but for some reason I can't seem to verify if that is correct.
http://img403.imageshack.us/img403/2056/cone1fw2.jpg
in the first one, i inserted h on the space of x, and on the second, 0 on the space of x. But I'm really not sure if that is correct, or if I should start over.
However, this is not similar to A, and I therefore need to make it smaller, if possible.

It would help if you showed more steps in your work. I ran through the calculation and get equation C, which your result is not equivalent to.

What did you have immediately after you evaluated the integral? Watch your algebra closely.

 

[Keba]

Right before the other calculation, I had this:
http://img108.imageshack.us/img108/232/cone2bu9.jpg
so, it is before I multiplied with pi.
I believe I used the solve function on my texas ti-89 calculator in order to get to the last part.
Is this what you meant?

 

[Keba]

Well, thank you for helping me dynamicsolo. I did get a step closer to the goal, and for the rest, I plan to ask a teacher tomorrow. I will go to bed now as it is 22:49 here. I will mark this as solved, and, thank you again dynamicsolo.