Volumes Q. (1 Viewer)

[Trev]

Pymble Ladies College 2001 Trial
4b) The area enclosed by the curves y=1/x², y=1/x and x=1/10 is rotated about the y-axis. Use cylindrical shells.

I can't find the part enclosed by the curves....
Thnx.

 

[Trev]

I don't have the answers.
I just want to know where it is enclosed, because it doesn't seem to be enclosed to me it just goes onto infinite...?

 

[speed2]

iam probably wrong but is da answer 81/200 pi units cubed??

 

[speed2]

well da curves intersect at x=1 right so the area is inclosed between x=1 and x=1/10

 

[Trev]

Urgh, me idiot. Thanx.

 

[speed2]

post up ur answer when ur done

 

[NT-social]

do u have da answer...b cause i have an answer but if its wrong u noe i dont wanna embarrass myself....

 

[speed2]

NT-social is ur answer same as mine (81pi/200) cause if it is were probably wrong. if not ur probably right.

 

[NT-social]

V={2.∏.x.(y2-y1).dx

{=intergrate...between x=1/10 and x=1

V=2∏{x(1/x-1/x2)dx
V=2∏{1-1/x .dx
V=2∏[x-ln(x)]... 1/10<x<1
...skip a few lines of working...
=2∏(9/10 - ln(10)) u cubed

 

[NT-social]

soo wat'dyo say? seems right?

 

[speed2]

V={2.∏.x.(y2-y1).dx

isn't it V={∏.x^2.(y2-y1).dx??? cause its lyk V=∏r^2y

 

[NT-social]

but for da cylindrical shels method...its 2∏xy.dx
for slices method it would have been squared

ya?

 

[Jase]

yep

...
...

 

[speed2]

but for da cylindrical shels method...its 2∏xy.dx
for slices method it would have been squared

ya?

urgh, as u can tell i havn't been revising on 4u!