Volume of Solid: Use Horizontal Rec?

[Miike012]

Problem:

Find the volume of the solid:

y = 2 - x/2 bounded by y = 0, x = 1, x = 2.

Answer: 19pi/12... I already know how to get the answer but...

what if wanted to use horizontal rec? For instance If I am using the vertical rec... the radius would be y = 2 - x/2... but if I use the horizontal rec would the radius be x = 2(2 - y) ? I tryed this value and integrated from y = 0 to y = 3/2... but did not get the correct answer...

Is it not possible to get the correct answer using horiz. rec?

 

[SammyS]

Problem:

Find the volume of the solid:

y = 2 - x/2 bounded by y = 0, x = 1, x = 2.

Answer: 19pi/12... I already know how to get the answer but...

what if wanted to use horizontal rec? For instance If I am using the vertical rec... the radius would be y = 2 - x/2... but if I use the horizontal rec would the radius be x = 2(2 - y) ? I tryed this value and integrated from y = 0 to y = 3/2... but did not get the correct answer...

Is it not possible to get the correct answer using horiz. rec?

Are you rotating this trapezoid around the x-axis to form the solid of revolution?

If so, then integrating w.r.t x is the disk method.

Integrating w.r.t. y is the shell method (cylindrical shells), so the radius is y itself. You will have to break the integration up into sum of two integrals.

 

[Miike012]

Yes I am rotating across the x-axis. So is it possible to use horizontal rec?

 

[Miike012]

Where can I learn about the shell and disk method? My teacher didnt mention these techniques.