4 unit extension 2 genious's need a question answered, thanks! (1 Viewer)

[dtv4_8]

hello guys,

just need some help with 4 unit, thanks heaps.

1. The region bounded by the curve y=x^2, y=(x-2)^2 and the x-axis is rotated about the line x=2. Use the method of cylindrical shells to find the volume of the solid.

its worth 5 marks, answer is 4pi/3 cubic units

 

[me dumb]

i got 8pi/3
what did i do wrong

 

[me dumb]

i went 2pi(integral)between 2 and 0, x^2(2-x)
=2pi[2x^3/3-x^4/4]between 2 and 0
simplify i got 8pi/3

 

[Aerath]

I got 4pi/3. I believe you need to split the volumes up into two different volumes. I rotated it around x = 0, which is the same as rotating it around x = 2. If you want, just post and I'll do it again, rotating it around x = 2.

 

[shaon0]

I got 4pi/3. I believe you need to split the volumes up into two different volumes. I rotated it around x = 0, which is the same as rotating it around x = 2. If you want, just post and I'll do it again, rotating it around x = 2.

Yeah, you have to split it up into two volumes. If you don't do that, you won't have a consistent height as a function of x when setting up dV.

 

[gurmies]

Yeah, I tried this question last night, and it occurred to me that you have to split this up. For some reason I didn't get the right answer though...

 

[Trebla]

You have to split it because the height of the shell is not always on the same curve. On one side, the height is on the curve y = x² and on the other side, it is on y = (x - 2)²

 

[Revacious]

i made the exact same mistake for about 2 hours in a row yesterday, and couldnt figure out where my stupid mistake was.

asking for shells for something with multiple curves is gay

 

[dtv4_8]

Hey thanks guys for all your help, special thanks to Aerath really appreciate it

 

[blaze.bluetane]

Asking for shells to answer that is quite painful...
The easier way is slicing

Just FYI dtv4_8....

quite simple really. much easier

 

[dtv4_8]

Ahhh yes thats a great way as well, thanks very much blaze