Paging Baseline Bum

[E20]

Or anbody else that is a 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: [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: '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 a 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=4putF...eature=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: '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 a 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=4putF...eature=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 , a math professor

[baseline bum]

, 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]

, 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........

[Nbadan]

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