Question

can someone help me,
washers/ disk method of
y^3 = x, y=0, x=1 about the y-axis?

Answer 1

first write the equation in terms of y= ....

Answer 2

y=x^3, I keep getting pi over seven and its 6pi over 7

Answer 3

did you change your equation in the question?

Answer 4

what do you mean?

Answer 5

i thought the equation originally said y^(1/3)=x but know it says y^3=x

Answer 6

i could have just saw in wrong sorry

Answer 7

i worked it out too and got pi/6

Answer 8

can you show me?

Answer 9

it's like pi(y^3)^2 and then i integrate and its 1/7 y^7 and i plug in between 1 and 0 and get pi over seven ?

Answer 10

yep thats what i did

Answer 11

where does the six come from?

Answer 12

oh I'm sorry, thats supposed to be a 7

Answer 13

the answer according to the shell method is 6pi over seven.

Answer 14

so for the shell method

integral of (2*pi*x*x^1/3)dx = 2*pi*x^(7/3)*(3/7)=6pi/7

Answer 15

if you use different methods are you supposed to get different answers?

Answer 16

no

Answer 17

could you show me the shell way of solving it, to get 6 pi over 7?

Answer 18

integral of (2*pi*x*x^1/3)dx = 2*pi*x^(7/3)*(3/7)=6pi/7

Answer 19

do you need it broken down more

Answer 20

sorry i meant the washer way.

Answer 21

oh ok

Answer 22

just by the washer method because when oh okay

Answer 23

well when your adding up washers the volume is pi*r^2*h
for the height its infinityls thin so h = dy.
the radius is your distance from the x axis so y^3.
your going from y=0 to y=1
so its integral of (pi*(y^3)^2*dy)= pi*y^7/7=pi/7

Answer 24

thats what i get at least

Answer 25

but the answer is 6 pi over 7, you don't know why there is a different answer?

Answer 26

i really don't. im not sure, but i believe im doing the method correct.

Answer 27

me too, okay well thanks for giving it your best attempt. i'm stymied.

Answer 28

sorry

Answer 29

wait a second,

Answer 30

if you look at the graph of the function you'll find when you are doing the washer methed you get the volume whats above the curve, but the shell method will give you the volume under the curve

Answer 31

so they will be different answers

Answer 32

at least the way we set them up.