Question

Find the volume of the solid generated
by revolving x+y^2=16 and x=0
about the x axis.

Why must i use shell method instead of Disk

Answer 1

can you draw it up?

Answer 2

ok hold on

Answer 3

something like that I think

Answer 4

i dont see a "must" for this one

Answer 5

how do i put it into my calc to draw that

Answer 6

hmm, you might have to play in your: y= area

Answer 7

x+y^2 = 16

y^2 = 16-x

y1 = sqrt(16-x); y2 = -sqrt(16-x)

Answer 8

disc is just adding up the areas of circles from 0 to 16 using sqrt(16-x) as your radius

Answer 9

shell would be from 0 to your yintercept; 2pi y f(y)

Answer 10

or something like that

Answer 11

i did that

Answer 12

that is wat i get when i put sqrt(16-x)

Answer 13

http://www.wolframalpha.com/input/?i=y+%3D+sqrt%2816-x%29+and+y%3D-sqrt%2816-x%29

Answer 14

zoom out on your calculator

Answer 15

ok i got the top half

Answer 16

when x=0, y=4

\[2\pi\int_{0}^{4} y(16-y^2)dy\]
or
\[\int_{0}^{16}[\sqrt{16-x}]^2dx\]
should be the same

Answer 17

the bottom half is just using another y= slot for the bottom

Answer 18

ok wait so when i look at the the equation and graph it, how can i determine whether Disk or Shell method is better

Answer 19

forgot a pi ...\[\pi \int_{0}^{16}[\sqrt{16-x}]^2dx\]

Answer 20

better is not a math term

Answer 21

easier

Answer 22

better is: which one can you do more easily?

Answer 23

to me, they are equally as simple

Answer 24

how do i know its going from 0 to 4?

Answer 25

becasue you are only calculating it between the x=0 axis; whic is the y axis

Answer 26

when x=0; y^2 = 16, y = -4 and 4

Answer 27

the shell only cares about how far from the middle you go; so go from 0 to 4

Answer 28

so disk is from 0 to 16?

Answer 29

yep

Answer 30

Find the volume of the solid formed
by revolving the region bounded by the
graphs of y=x^2+1, y=0, x=0, x=1 about
the y axis.

Answer 31

how can i apply disk method to that?

Answer 32

draw it out and see what needs to be addressed