Question

Washer Method-Calculus
need help setting up problem

Answer 1

Find the volume if the region enclosing y=x+1, x=0, y=0, x=3 rotated about the y axis

Answer 2

@AccessDenied

Answer 3

I just want to verify my setup since I do not agree with the key provided

Answer 4

Sure. Are you able to post that setup?

Answer 5

ok I will post it

Answer 6

\[\pi \int\limits_{0}^{1}3^2dy + \pi \int\limits_{1}^{4}3^2-(y-1)^2 dy\]

Answer 7

key states 1 to 3 for the second integral, but I thought I had to use the y coordinates for dy problem

Answer 8

So I'll just draw a sketch first (those are always good)

We had y = x + 1. So x = y - 1. So indeed the outer radius is 3 and the inner radius is (y - 1).
Integral from 0 to 1 of 3^2 (the inner radius does not affect this) dy + integral from 1 to 4 ... yeah. that should be a 4.

Answer 9

ok thanks
now I a working on another one similar to this one
Same items except rotation is about the line x=3

Answer 10

key is telling me to set it up as a washer

Answer 11

I think it should be a disk

Answer 12

**for the first one** If you follow it through, you could probably make a geometric argument using volume of a cylinder of radius 3 removing volume of cone of height 3 and radius 3 just to check the answer.

Answer 13

so the solution for the first one is 27 pi with the geometric argument and yes the solution is exactly that

Answer 14

Aaand yeah, you should be using disks for that one. There would be no hole for the need of washers there. :)

Answer 15

thanks...... I knew the key was not 100% thanks once again

Answer 16

No problem! Sometimes they mess up. After all, its not their grade to worry about. :p