Question

calcII
how do you calculate y=2-2x on the first quadrant, if circled around the x-axis making a cone?
ans;4pi/3

Answer 1

make a drawing of the graph to start

Answer 2

have that in the book.

Answer 3

now draw in the figure and look for the radius of each disk

Answer 4

this is if you want to do disk method and integrate along y

Answer 5

slope...
\[\theta=\tan^{-1}(-2)=?\]
TuringTest, the diagram is wrong.

Answer 6

x axis.

Answer 7

sorry

Answer 8

actually much easier this way imo

Answer 9

ah yes x=1, I am senile at the moment it seems :P

Answer 10

what is the radius of each disk then?

Answer 11

half of the distance between the curves?

Answer 12

electrokid, you have no idea what your talking about.

Answer 13

and it's 2-2x.

Answer 14

@rosho yes, so the area of each disk then?

Answer 15

pir^2

Answer 16

and substituting for what we know r to be, what is that in terms of x ?

Answer 17

pi(2-2x)^2

Answer 18

yes, that is the area of each disk. Now we add up all the disks by integration to find the volume.
what will be the bounds of the integral?

Answer 19

that's where i got stuck.

Answer 20

well, you are integrating along x. How far can we go in the x direction before we hit the line 2-2x in quadrant 1?

Answer 21

oohh.

Answer 22

0,1

Answer 23

yep, now proceed and integrate :)

Answer 24

V=int{0,1}((2-2x)^2)pidx
correct?

Answer 25

yes