Using slice (1 Viewer)

[DcM]

help..

using slice fin the volume of the solid obtained by rotating the region

{(x, y) : 0 <= x <=sqrt 6, 0 <= y <= 6x² - x⁴ about the y axis.

=) thanks

 

[gman03]

This is my attempt:

The maximum y is when x = sqrt(3) so y = 9

Hence volume is I{0->9} Pi*(x₁² - x₂²)dy

now y = 6x² - x⁴

so (x²)² - 6(x²) + y = 0

Solving quadratically we get:
x² = [6 +/- sqrt(36-4y) ] / 2

so x₁² - x₂² = sqrt(36-4y)

so V = I{0->9} Pi * sqrt(36-4y) dy

and then i get V = 36 Pi

Have not done a volume question for a year, pls verify my result. Thanks

 

[gman03]

I'll come back and fix my notations...

(Edit: Fixed)

 

[:: ck ::]

yes i got teh same...

 

[DcM]

oh and also in q. 7

find volume enclosed within the circle (x - 1)² + y² = 1 about the y axis.

this is what i did..
r = x
R = 2 - x
.: A = pi * (4 - 4x)
.: dV = pi (4 - 4x) dy
V = 2 pi * I {0 -> 1} +- 4 sqrt(1 - y²)dy
..since x = 1 +- sqrt(1 - y²)

so from here....how do u know if to use +ve or - ve ??

 

[:: ck ::]

...

well let v = 1 + sqrt(1-y^2)
u = 1 - sqrt(1-y^2)

now area of a typical slice will be pi(v^2-u^2)

use both .. lol

ans i got is 2pi^2

 

[DcM]

noo...
i get wat u mean but
like do u follow wat i did??
so like if i was where i was up to...wat wud u do?

haii...ill show u tmw..

lol i realised nearli everything i post up...u say some crap..

y sound so pro for lolz....grr...trials coming up..u betta not beat me... >.<

 

[:: ck ::]

i dun sound pro i just waste time here to help ppl for a confidence boost

i will steal ur ranking and attempt to steal addisons too to come 2nd !!! >=D

but i doubt i can get 2nd =|

we better get a hard trial... or ill be ultra pissed off

and why cant u follow on from wot ur doing?? ur on the rite track

just integrate wif respect to y? o.o

 

[gman03]

Originally posted by DcM
how do u know if to use +ve or - ve ??

If my memory serves, in slicing somewhere we will be ask to find the difference of x₁ and x₂ or something like that... If x happens to have some +/- sqrt() terms then you choose the difference to be positive...

Hope that clarifies you.