Find the mass and center of mass of "lamina" ?

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CalleighMay

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Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help!

I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is our last week of class after our final exam so my professor is taking this time to give us a preview of what we will be learning in the fall semester in Calc III (since this is the same professor). Every Tuesday class our professor gives us a few problems from future sections and asks us to "see what we can come up with" and to work together to find solutions. The following Tuesday he asks us to discuss the problems as a class, seeing which ones of us know our stuff =P

Basically, i want to ask you guys what you think about these problems as i do them along before i have my discussion. I really want to make a lasting impression on my professor by "knowing my stuff" -to show him i can do it! All's i need is a little help! Would you guys mind giving me some help?

We are using the textbook Calculus 8th edition by Larson, Hostetler and Edwards and the problems come from the book.

The problem is on pg 1015 in chapter 14.4 in the text, number 14. It reads:

Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given density or densities (Hint: some of the integrals are similar in polar coordinates).
And it gives:
y=x^3, y=0, x=2, p=kx

(the p looks a little different, most likely represents something else, and the k really is a k, not to be confused with that wavelength symbol lol)

I looked at similar problems in the same section and came up with the following for this one:

I first graphed the equations on the same coordinates.
I think im supposed to take the integral from (0 to 2) of the integral from (0 to x^3) kxdxdy? or kxdydx? (something about horix simple or vert simple??)

And then i'm confused as to what to do next, even if i was sure what i have so far is correct.

Any further help would be greatly appreciated. Thanks guys
 
That is the Greek letter RHO. It is used for density. Not ROE. It's not fisheggs, but a Greek letter :D :wink:

\(\displaystyle m=\int_{0}^{2}\int_{0}^{x^{3}}kx dy dx\)

\(\displaystyle M_{x}=\int_{0}^{2}\int_{0}^{x^{3}}kxy dy dx\)

\(\displaystyle M_{y}=\int_{0}^{2}\int_{0}^{x^{3}}kx^{2} dy dx\)

\(\displaystyle \overline{x}=\frac{M_{y}}{m}\)

\(\displaystyle \overline{y}=\frac{M_{x}}{m}\)
 
Sorry if i seem stupid but what does that mean i should do? =/ Should i take the double integral for each value you have there?

Basically, will my answer be one single answer or a value for each m, Mx, My, x and y? Or do i need each of those values to combine one single answer.

Thanks :) Just confused as to what i'm even looking for
 
Shouldn't i end up with a numerical answer? How do i proceed here? Or do i leave this the way it is?
 
Here we have it again. We can put the food on the table, but eventually you will have to reach out and pick some up. It's very difficult to get those little spoons though the computer screens.

Please find a better way to go. Guessing, total dependence, lack of direction, unable to tell what the question is asking, not very good at notation, only passingly interested in the subject matter, -- really, what is it that you are trying to do? You don't seem to know, despite your description of your situation.
 
tkhunny, all the extra effort i am putting into these problems is just for "me". He doesn't expect us to know how to do it, he's just giving us a chance to look it over before we have it next semester (which is 2 weeks away). In the next few weeks i will go over it even more in depth to a level of better understanding, but for this week my main goal is to show my professor i am understanding it "now". It took me a while to get started this summer (because my teacher in HS for calc I didn't do the best job) but i am getting the hang of it now.

I understand it is hard for everyone here to be able to help me with my lack of knowledge, that's why i explained in the beginning what my situation is, that i haven't been taught any of this stuff. It is like telling 5th graders to understand pre-algebra, this stuff is hard! =/

I would never expect you guys to be able to teach me this stuff via computer posts in 5 days, i am just grateful for any input you "can" offer however. At this point, since i have class in 3 hours, the simple worked out solution would est help since i can follow it and be able to relay it to my group...

Thanks, you guys :)
 
CalleighMay said:
my main goal is to show my professor i am understanding it "now".
Click to expand...
But you don't "understand it 'now'", as your replies have repeatedly shown. In order to learn the material, you need to start studying at some point. And "study" does not mean "look for an exactly-the-same example to copy from" or "get some tutors to do it for me, telling me which part is the answer, so I can fool my [apparently staggeringly-stupid] professor".

If you would like to start contributing something to this process, that would be great. But we simply cannot do the studying for you, nor can we "spoon-feed" the material to you. The reason it will take many chapters in the book, and many weeks in a semester, to cover this material, is in part that WE CAN NOT TEACH THIS MATERIAL IN "FIFTY WORDS OR LESS" OR IN SOME OTHER QUICKIE FORUM POST.

It would be really nice if, at some point, you gave evidence of having taken any of this to heart. Thus far, we see only efforts to "put one over" on somebody you must not respect very much.

Eliz.
 
In the next few weeks i will give a great deal of effort in learning this material better, but for now, considering i have 3 hours before class, i cannot do so. My professor isn't collecting our answers, he asks us to look at the problems and we will discuss them in small groups in class tonight. We then play a "game" of which group has gotten the closest. It is solely for "making math fun"- his goal is to get us involved without having to worry about being graded.

I just want to be able to present a correct answer. Even if i no not understand it today, i will before classes start in 2 weeks. I guarantee there isn't another person in my class that has done half the work trying to get help from others. Since attempting these problems is not graded, no one else is even looking at them.

I know i cannot learn the stuff in a week, i just want to be able to have the solution for presentation and so i can follow them...
 
Hey guys, can someone give me the full solution please? We had class last night and he didn't really explain them but i would like to know the answers.

Thanks!
 
CalleighMay said:
Hey guys, can someone give me the full solution please? We had class last night and he didn't really explain them but i would like to know the answers.

Thanks!
Click to expand...
You have to show us that you are at least trying - and are capable of attending these classes that teach at this level.

The copy of the book that I have (2 nd edition) has very good example problems - almost exactly like the problem posted - I would assume 8 th edition will have similar/same example problems.

Read through those - copy one of those problems onto these pages to show that you are at least looking at those - then I would work with you....
 
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