Question

Find the volume generated by rotating the region enclosed by the graphs of f(x)=x^2 & g(x)=x about the y-axis.

Answer 1

when you see something like "rotated about the y axis"
get the equations you were given in terms of y
so y = x^2 --> x = ?
and y = x --> x = ?

Answer 2

that's all i have sleepy head

Answer 3

? you mean you don't know how to get it in terms of y?
just solve for x

Answer 4

really?

Answer 5

yep :P

Answer 6

x^2 = sqrt(y), -sqrt(y)
x = y

Answer 7

yep :) and find the point where they intersect

Answer 8

lol :o
let me try

Answer 9

(0,0) :S

Answer 10

and... ? :P

Answer 11

hmm... make those the min and max right?

Answer 12

lol there's another point I mean :P

Answer 13

lol oops. shoud I add the originals?

Answer 14

oh (1,1)

Answer 15

yeah lol ;)

and if you rotate it, you'll get a washer >.>
so pi times the integral from 0 to 1 of y minus y^2 dy

the 0 came from (0,0)
the 1 came from (1,1)
the y was from (root y)^2 = y
the y^2 was from (y)^2 = y^2 :P

Answer 16

so min = 0
and max = 1

Answer 17

yeah :)

Answer 18

k one sec

Answer 19

-2 pie / 15?

Answer 20

hmmm that's not quite what I got...

Answer 21

:( darn

Answer 22

2pi/15?

Answer 23

erm...
integral of y-y^2 --> (1/2)y^2 - (1/3)y^3

Answer 24

hey it's jiggly puff!!
k one sec.

Answer 25

i got a big number. I took "y-y^2" as y to y^2

Answer 26

huh? y-y^2 as in y minus y squared

Answer 27

lol my brain hurts one sec

Answer 28

9/64

Answer 29

>.>
if you just plug in 1 into (1/2)y^2 - (1/3)y^3

http://www.wolframalpha.com/input/?i=pi+times+the+integral+from+0+to+1+of+y+minus+y%5E2+dy

Answer 30

pi/6??

Answer 31

yep :)

Answer 32

<3