volumes q (1 Viewer)

[kony]

cambridge 6.2 q7 and 8. page 192

so you have to use cylindrical shells method to find the volume generated by the circle (x-1)² + y² = 1 about the y axis.

the problem is that i get to the bit where you need to integrate xydx

but y is sqrt(2x - x²)

so overall, integrating x.sqrt(2x-x²)


i have no idea how to integrate this, even though i've done integration.

help please?

edit: oh yeah, q8 is similar. have to integrate x.sqrt(x-x²) i think.

 

[kony]

aaaah i see.

i completed the square but i thought it was necessary to have trig functions outside the sqrt to be able to be "used up".

thanks!

 

[kony]

turns out i still got an incorrect answer.

can someone please do the full working?

 

[Mill]

This is a very similar question.

It also supplies a second method for doing the question.





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[kony]

thanks for the info.

in the first attachment, torus q, inside the red box, how do they know the second integral is 0? is it because the integrand is odd?

and in the second attachment, alternative method, how did they integrate the first integrand? or did they just skip some steps?

thanks again.

 

[Mill]

There are steps missing that would be taught in the class.

First question: odd integrand.

Second question: let u = 1 - (x-2)^2.
If you are super awesome, you could do this without the substitution though - it's not mandatory.

 

[kony]

yeah i see there's a slight manipulation needed.

i suppose this is the general method to do any torus problem, since you'll always encounter such an integral.

thanks for the help.

 

[comman01]

ohhh so thats how you do it! ive been stuck on those 2 questions...

that method of integrating is insane! thanx 4 the advice!