Volumes Help! (1 Viewer)

[fahadmumtaz88]

Guys i'd much appreciate if u cud help me in solving this volumes question, once agian the answer seems to be different to mine. Anyways, i'd give it to you guys
thanks. i've attached the diagram. The question is:


The area common to the circles x^2 + y^2 = 16 and x^2 + y^2 = 8x is revolved about their common chord.

Find the volume.

 

[brett86]

 

[lum]

hmm, i tried doing it by shells and ended up with a intergral of from 0 to 2, root(8x - x^2) (the rest is alrdy intergrated)

any idea how do do that?

 

[FinalFantasy]

hmm, i tried doing it by shells and ended up with a intergral of from 0 to 2, root(8x - x^2)

any idea how do do that?

int. sqrt (-(x²-8x+16)+16 ) dx=int. sqrt (16-(x-4)² ) dx
let (x-4)=4sin@
x=4sin@+4
dx\d@=4cos@

int. sqrt (16-(x-4)² )dx=int. sqrt (16-16sin²@)* 4cos@ d@
=int. 16cos@sqrt(cos²@) d@
=16int. cos²@ d@
=8int. (cos2@+1) d@
=8 [(1\2)sin2@+@]
=4sin2@+8@+C
then use sin@=(x-4)\4 to simplify it more

 

[FinalFantasy]

^ oh just realise u have terminals... well then just use them

 

[lum]

thanks ff! really appreciate it

another stupid qs, u know when u sub in x=4sin@+4, and u get the new limits, say...
at x = 0, sin@ = -1 , now which quad do you take for the new limit? is it always just between -n/2 and n/2? but theoratically shouldn't 3n/2 be rite too? but 3n/2 will giv a different answer than -n/2.

weird how this has never been a problem in all those other sin/cos susbstitution qs

 

[brett86]

hmm, i tried doing it by shells and ended up with a intergral of from 0 to 2, root(8x - x^2) (the rest is alrdy intergrated)

any idea how do do that?

 

[lum]

thx brett for the geometrical way

 

[FinalFantasy]

thanks ff! really appreciate it

another stupid qs, u know when u sub in x=4sin@+4, and u get the new limits, say...
at x = 0, sin@ = -1 , now which quad do you take for the new limit? is it always just between -n/2 and n/2? but theoratically shouldn't 3n/2 be rite too? but 3n/2 will giv a different answer than -n/2.

weird how this has never been a problem in all those other sin/cos susbstitution qs

hahaha i don't know, just try it out and c

 

[lum]

meh, i doubt anything like that will be there tomorrow

man, i hope i do well

 

[FinalFantasy]

hahaha, ye doing cssa?

 

[lum]

everyone is! , i just realised how retarded my qs about limits was, don't worry about it.

 

[FinalFantasy]

not everyone's doing the cssa...

 

[yrtherenonames]

Just out of interest, does anyone know how many kiddies do these syndicated papers?

 

[lum]

arghh, i was just kiddin, but still, it'd be the most used paper for maths, (i'm guessing)