Question

find the volume of the solid generated by revolving the line x=-4.The region bounded by the two parabolas x=(y-y^2),x=(y^2-3).

Answer 1

sounds like a torus...

Answer 2

need to figure out the solution to the system of equations to know what our "bounds" are gonna be...

Answer 3

i got an idea, but its just to early in the morning to get it right in me head.....

Answer 4

the bounds for the integral are gonna be [-1,(3/2)]

Answer 5

That is an odd region...is it the odd oval shape?

Answer 6

(S) y-y^2 dy = (1/2)y^2 -(1/3) y^3 |-1-3/2

Answer 7

its a funky shape fer sure :)

Answer 8

use circular ring method..

Answer 9

F(-1) = 5/6

Answer 10

That shape isn't circular...

Answer 11

i know the answer but i dont know the solution..

Answer 12

F(3/2) = 9/8

Answer 13

v=85.902 cubic units

Answer 14

your one step ahead of me then :) I am just trying to find the area of the shape

Answer 15

.plz help me..

Answer 16

for F(x) + get an area of 7/24....which could be totally wrong, but ill see :)

Answer 17

I don't understand exactly which region he is asking for...

Answer 18

G(x) = (S) y^2-3 dy = (1/3)y^3 -3y | -1,(3/2)

Answer 19

These are the graphs
http://www.wolframalpha.com/input/?i=x+%3D+y-y^2%2C+x%3D+y^2-3%2C+x%3D-4

Answer 20

Why does this site suck at showing links...

Answer 21

the region for the area is between y=-1 and y=(3/2)

Answer 22

So it's the odd oval shape in the center
http://www.wolframalpha.com/input/?i=x+%3D+y-y^2%2C+x%3D+y^2-3

Answer 23

i solved the system of equations and got y=-1 and y=(3/2) as solutions

Answer 24

Yes i see those bounds

Answer 25

If I did it right; the area of F(x) = 7/24. Now I need to subtract area of G(x) right?

Answer 26

G(-1) = 8/3

Answer 27

So where exactly does the line x = -4 come in then

Answer 28

you spin the area around x=-4 to find the area of the torus shape

Answer 29

Oh that's the center

Answer 30

i hope its the center :)

Answer 31

G(3/2) = -27/8 if Im doing it right :)

Answer 32

where should i put the strip??is it horizontal or vertical?

Answer 33

area of G(x) = -145/24 ?


Horizontal I beleive

Answer 34

well it can't be

Answer 35

total area of shape is F(x) - G(x) = 152/24

Answer 36

how do we spin it? multiply by circumference of the circle?

Answer 37

integrate from 0 to 2*pi

Answer 38

i thought

Answer 39

I can find the area between curves alright, but after that I get lost :)

Answer 40

Area = 38/6 = 19/3...thats as far as I can reduce it; if its right

Answer 41

how do we integrate the spin? Do we need to find the domain of the area are anything?

Answer 42

I'm not exactly sure

Answer 43

lol.....comeon..your smarter than me for sure :)

Answer 44

i thought it was the integral from 0 to 2*pi, but that wouldn't make much sense in this case

Answer 45

What about using the ring method

Answer 46

That would probably just be much more difficult

Answer 47

not that versed in the ring method...

Answer 48

sounds like we'd integrate with respect to the radius....

Answer 49

yes the inner radius would be the maximum for the first equation, and the outer radius would be the maximum for the 2nd i believe

Answer 50

gotta go back and find the bends then :)

Answer 51

one of those bounds is x=1/4

Answer 52

is that right? y-y^2 x'=1-2y=0 y=1/2. .5-.5^2 = .25 x=1/4 right?

Answer 53

My brain hurts lol. Okay so you're deriving y-y^2, solving for y, and plugging it back in?

Answer 54

y^2 -3 x'=2y=0 y=0 other bound is x=-3

Answer 55

Yeah that seems right

Answer 56

yep, only thing I can do :)

Answer 57

sp we got our bends at x=-3 and x=1/4....now what?

Answer 58

spin it at x=-4 somehow

Answer 59

each slice is spin from -3 to 1/4 in dx increments and then add them all up

Answer 60

Im confused on the area

Answer 61

make it easier and spin add 4 to x so that we have the middle at 0 and our limits at 1 and the other at 4.25

Answer 62

Yeah that's what i did actually :)

Answer 63

which area :) the area between the curves?

Answer 64

yes, the integral of x = y-y^2 would give the area under the parabola, but how would you remove the sections on the sides to get the torus

Answer 65

Or i should say...to the right of the parabola

Answer 66

the two equations meet at the points -1 and 3/2; so these are the bounds we use. to find the area right?

Answer 67

Ok i see

Answer 68

back in algebra here :) when y-y^2 = y^2-3 we get solutions to the equations :)

Answer 69

2y^2 -y -3 =0

(y-...)(y+....)

Answer 70

I use that to find the area of F(x) and G(x) then: F(x)-G(x) gives us the area we need

Answer 71

now, since we are talking about spinning a circle; do we (S) 2pi(x)(area)? dx

Answer 72

it should be the same concept as finding the area between curves; use the lower and upper bounds of x and subtract them?

Answer 73

cant hurt to try:

(S) 2pi(x)(19/3) dx = 19pi(x^2)/3 | 1,4.25

Answer 74

114.39583333(pi) - 6.3333333333(pi)

Answer 75

I get 108.0625 pi....but am I right?

Answer 76

ill need alot more practice for this I guess :)

Answer 77

v=85.902 cubic units is what the person said to begin with; and that doesnt match mine

Answer 78

Yeah it doesn't, my brain is too fried for this right now, I've got diff eq in 5 hours, best of luck though

Answer 79

the key lies in the y axis. distance from the y axis bounds i think..not the x-axis

Answer 80

what is the integral of
1/((x+2)√(x+3))

Answer 81

im wrong somewhere :)

Answer 82

i need more practice on integrals... .

Answer 83

have you intergrated by parts?

Answer 84

yeah...but dunno if its correct

Answer 85

did you do it more than once?

Answer 86

(S) 1/x+2 dx = ln(x+2) that much works out

Answer 87

i gotta get some sleep :)....chat with ya later think...

Answer 88

okay amistre...btw u have taken u=1/x+2?