Paging Baseline Bum

[E20]

Or anbody else that is hella good at Math, please respond to this thread!

[midgetonadonkey]

I'm good at math. I can do my times tables.

[E20]

I think ShoogarBear is good, maybe he can help.

[midgetonadonkey]

What's the problem? I can help.

[E20]

Find the volume of the solid whos base is the region bounded between the curves y=x, and y =x^2 and whose cross sections perpendicular ot the x-axis are squares.

Forumla to use: http://mathworld.wolfram.com/images/equations/Integral/equation2.gif[f(x)]^2-[g(x)]^2

a=0
b=1
f(x)=x
g(x)=x^2

I need to know if my answer is the right one. I'm getting 2/15.

[midgetonadonkey]

What does the big S mean?

[E20]

Ugh you integrate from B to A (anti-differentiate), basically you square the given functions and then anti-differentiate.

[midgetonadonkey]

Does this involve the FOIL method? Because I never understood the FOIL method.

[DisgruntledLionFan#54,927]

I got pi.

[E20]

I got pi.
Um Well I'm using the washer method which involves PI, but this particular problem states that the cross sections that are perpindicular to the x axis are squares, so it can't have Pi in it.

Does this involve the FOIL method? Because I never understood the FOIL method.
Nope.

[midgetonadonkey]

What would Stallone say?

[Mr.Bottomtooth]

The answer is Chuck Norris. But then again, he's always the answer.

[E20]

What would Stallone say?
There is that famous quote in Rambo III, where him and Trautman are surronded by Soviets and Trautman says should we do what they want? And he replies: Fuck 'em. In that bad ass way, that line is probably the baddest thing that has ever hit american cinema, so that is what he would say.

BTW the internet sck ass, I've been searching for answers to this problem for 15 minutes and nothing. This is hella basic too, so I don't know why this isn't on the internets.


**For a more visual example watch stallone say it:
Starting at 8:40
http://www.youtube.com/watch?v=4putFVscZ0E&feature=related

[midgetonadonkey]

There is that famous quote in Rambo III, where him and Trautman are surronded by Soviets and Trautman says should we do what they want? And he replies: Fuck 'em. In that bad ass way, that line is probably the baddest thing that has ever hit american cinema, so that is what he would say.

BTW the internet sck ass, I've been searching for answers to this problem for 15 minutes and nothing. This is hella basic too, so I don't know why this isn't on the internets.


**For a more visual example watch stallone say it:
Starting at 8:40
http://www.youtube.com/watch?v=4putFVscZ0E&feature=related

If you were smart you would've figured it out by now.

[E20]

If you were smart you would've figured it out by now.
I got 2/15, but my punk ass teach says otherwise.

[midgetonadonkey]

I got 2/15, but my punk ass teach says otherwise.

It sounds like you are the punk ass.

[E20]

It sounds like you are the punk ass.
I'm actually the most civil mannered person you will meet. This internet persona is a facade.

[midgetonadonkey]

I'm actually the most civil mannered person you will meet. This internet persona is a facade.

Civil mannered or not, you suck at math.

[marini martini]

try turbo tax

[baseline bum]

2pi /15

Cross sections perpendicular to the x-axis are squares means you're rotating about the x-axis.

0 <= x <= 1 implies ymax = x, ymin = x^2 for each thin washer, since x <= x^2 for 0 <= x <= 1

Each thin washer has volume:

dV = (pi*ymax^2 - pi*ymin^2) dx
= (pi * x^2 - pi * (x^2)^2) dx
= (pi * x^2 - pi * x^4) dx
= pi * (x^2 - x^4) dx

Integrate over x from 0 to 1 to get 2pi / 15

[E20]

2pi /15

Cross sections perpendicular to the x-axis are squares means you're rotating about the x-axis.

0 <= x <= 1 implies ymax = x, ymin = x^2 for each thin washer, since x <= x^2 for 0 <= x <= 1

Each thin washer has volume:

dV = (pi*ymax^2 - pi*ymin^2) dx
= (pi * x^2 - pi * (x^2)^2) dx
= (pi * x^2 - pi * x^4) dx
= pi * (x^2 - x^4) dx

Integrate over x from 0 to 1 to get 2pi / 15
Hmmmmmmm funny because my book says when they are squares their should be no Pi, so my answer was just 2/15. I'm gonna have to talk to the Professor cause she stated the same thing.

[marini martini]

2pi /15

Cross sections perpendicular to the x-axis are squares means you're rotating about the x-axis.

0 <= x <= 1 implies ymax = x, ymin = x^2 for each thin washer, since x <= x^2 for 0 <= x <= 1

Each thin washer has volume:

dV = (pi*ymax^2 - pi*ymin^2) dx
= (pi * x^2 - pi * (x^2)^2) dx
= (pi * x^2 - pi * x^4) dx
= pi * (x^2 - x^4) dx

Integrate over x from 0 to 1 to get 2pi / 15

No shit, a math professor :toast

[baseline bum]

Shit, I see what you mean now by cross sections being squares.

width on the z-axis is equal to the height (where x-axis is length, y-axis is height, and z-axis is width of the solid), and there's no rotation.

i.e., w = x-x^2 from 0 to 1

each volume element has volume
dV = w*h dx = h^2 dx = (x-x^2)^2 dx
V = Integrate((x-x^2)^2) dx), from x=0 to x=1
= Integrate((x^2 - 2x^3 + x^4) dx), from x=0 to x=1
= 1/3 - 2/4 + 1/5
= 1/30

[E20]

Shit, I see what you mean now by cross sections being squares.

width on the z-axis is equal to the height (where x-axis is length, y-axis is height, and z-axis is width of the solid), and there's no rotation.

i.e., w = x-x^2 from 0 to 1

each volume element has volume
dV = w*h dx = h^2 dx = (x-x^2)^2 dx
V = Integrate((x-x^2)^2) dx), from x=0 to x=1
= Integrate((x^2 - 2x^3 + x^4) dx), from x=0 to x=1
= 1/3 - 2/4 + 1/5
= 1/30
I see my problem now. The base of a square whose volume you are finding is h^2 and rather than foiling I just distrubted the power rather than foiling the thing out. Damn........ :bang

[Nbadan]

......wait till he tries some washers......

[Nbadan]

...by the way, I get 2/15.....

[baseline bum]

Show your work, sucka

[Nbadan]

Not me...I've seen your work...but....to (find the volume of the solid whose base is the region bounded between the curves y=x, and y =x^2 and whose cross sections perpendicular to the x-axis are squares)....in order to form a 'solid' to find 'volumes' shouldn't he rotate either around the x or y axis?

[baseline bum]

Nah, that would make the cross sections washers.

[Nbadan]

Nah, that would make the cross sections washers.

To find the volume though wouldn't you make the cross-sections of the washers squares, (assuming your rotating around the y-axis)?

[E20]

To find the volume though wouldn't you make the cross-sections of the washers squares, (assuming your rotating around the y-axis)?
Since it is a square and to find the area of the square it two sides mutliplied together and since all the sides of the square are (x-x^2) it is (x-x^2)^2, and that's when you have to foil. I made the same mistake as you prior. I'm on finding arc lengths now. It's pretty tedious when they start giving you like [e^t(cost+sint)]^2+[e^t(cost-sint)]^2, that problem took a whole page.

[Nbadan]

...assuming that's true, then the answer is 2(pie)/15...

[E20]

...assuming that's true, then the answer is 2(pie)/15...
Since it is a square, it doesn't need pi, only clyinders/circles, when doing these types of problems. The answer is 1/30. You have to foil it, then integrate, then evaulate from 0 to 1.

[Nbadan]

.....maybe I'm just not seeing how those those two angles on a Cartesian plane can be squares....but if you say so....

[E20]

.....maybe I'm just not seeing how those those two angles on a Cartesian plane can be squares....but if you say so....
I don't really see it either. I don't visualize problems or see how they would look graphically, I just follow the directions on how to do them. :lol

[Nbadan]

...you have to be able to visualize math problems....wait till you get to set theory...

[baseline bum]

...you have to be able to visualize math problems....wait till you get to set theory...

Set theory requires a much stronger argument than calculus does, and requires incredible careful symbol manipulation and application of axioms. Set theory is a really cool subject of study though; especially when you get around to understanding what real numbers really are. Still, (abstract) algebra and probability are my two favorite subjects.

[baseline bum]

.....maybe I'm just not seeing how those those two angles on a Cartesian plane can be squares....but if you say so....

This is what the solid from the problem looks like:

http://img165.imageshack.us/img165/8167/76951147cq9.th.png

It looks the same from the side and from the top view.

The bright red is the side, the dark red is the top.

[Nbadan]

...all I remember is that it is difficult to do complex injections, surjections, and bijections without visualization.....and set theory comes right after Cal3...

[Nbadan]

..as long as we're having fun with math though....

Find the depressed cubic:

X^3 + 6X^2 + 8X = 1000

[E20]

Thank god I'm not taking that. I just need Cal 1 + 2 and some stats class. I've always wondered though how it would be like to be a Math major.

[baseline bum]

...all I remember is that it is difficult to do complex injections, surjections, and bijections without visualization.....and set theory comes right after Cal3...

Set theory for non-math majors? ZFC set theory is some pretty hairy shit for someone who's not a pure math major. It's certainly way too difficult for the average student to do having only done calculus up to vector spaces, linear transforms, series, and Stokes Theorem (I'm assuming that's what you mean by Cal3). You gotta have at least a class of analysis or abstract algebra to be in the kind of mindset to approach things in the axiomatic way that ZFC set theory requires.

[Nbadan]

Set theory for non-math majors? ZFC set theory is some pretty hairy shit for someone who's not a pure math major. It's certainly way too difficult for the average student to do having only done calculus up to vector spaces, linear transforms, series, and Stokes Theorem (I'm assuming that's what you mean by Cal3). You gotta have at least a class of analysis or abstract algebra to be in the kind of mindset to approach things in the axiomatic way that ZFC set theory requires.

They've broken it down to some prelim classes down here because too many people couldn't make the jump from Cal2 or Cal3 to the ZF Universe, so the very first classes focus on the axioms, set theory, the natural numbers, and then they jump to cardinality, equivalence class and relations and then into number theory and Euclidean algorithms and...yada...yada...

[baseline bum]

Thank god I'm not taking that. I just need Cal 1 + 2 and some stats class. I've always wondered though how it would be like to be a Math major.

What's your major?

[Whisky Dog]

Learn how to take orders, make money, satisfy a woman, and raise kids. Everything else is just gravy.

[to21]

Learn how to give orders, make money, satisfy a woman, and raise kids. Everything else is just gravy.
QFT

[E20]

What's your major?
I'm a pre-med taking my lower requirements right now (2nd semester of College so far). Organic Chemistry scares me more than Calculus 3. I guess I can tell that you are a computer science/engineer major.