Calculus 2 Find the volume problem

[hvidales]

Homework Statement

Find the volume: y=x, y=0, x=2, x=4; about x=1

Homework Equations

Washer method V= ∏∫ (R)^(2)-(r)^(2) dy

The Attempt at a Solution

0 to 4 is my a to b**

∏∫(from 0 to 4) of (1-4)^(2)-(1-y)^(2) dy

∏∫(from 0 to 4) of 9-(1-2y+y^(2)) dy

∏∫(from 0 to 4) of 8 + 2y - y^(2) dy

∏[8y+y^(2)-y^(3)/3](from 0 to 4)

∏[32+16-64/3]=80∏/3


That is my answer but I want to make sure that I got it correct. Thanks in advance!

 

[hvidales]

Hey people. So I reworked it and i got 76pi/3. Is this correct?

 

[lewdawgdude]

I got 24∏. With rotations about the x-axis it is usually easier to use cylindrical shells. It's much harder with washers, I don't even want to think about what you'd do for that. With cylindrical shells the integral would be from 0 to 4 of 2∏∫(x-1)x dx.

 

[hvidales]

Hey I ended up getting it. Thanks for taking the time to work it out.