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You are not logged in. #51 20130113 11:05:07
Re: The Structural Analysis  mathematics of the futureHi bob.
Is analog: Last edited by 21122012 (20130113 11:10:37) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #52 20130113 18:10:25
Re: The Structural Analysis  mathematics of the future
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #53 20130114 05:22:16
Re: The Structural Analysis  mathematics of the futureHi Bob! "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #54 20130114 06:56:28
Re: The Structural Analysis  mathematics of the futurehi 21122012, Now add them up Now, and this is the important bit, for a cylinder, every slice is the same size, so the pi r^2 term is constant as h varies. If V = 0 when h = 0 then C = 0 For a cone each slice is again a circle with a radius of r. But the circles are not all the same size. As h increases from o to H, the radius changes from 0 to R. So \pi r^2 is not constant. So the result is different. Do you understand now how integration works ? Add up the slices but take account of whether they are all the same size, or change as h changes. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #55 20130114 07:56:50
Re: The Structural Analysis  mathematics of the future
Everything is up to this point all is correct
I don't understand this thought!
Gallantly!
STOP!!! Here mistake!!! I constantly speak to you about it, but you don't hear me!!! It not algebra! At the left you have two independent variables therefore the result will be one. On the right two dependent variables therefore the result will be another. These two expressions aren't EQUAL! Use WolframAlfa, it will yield to you two various results! Look this. You equate two red areas to which shooters point. These areas aren't equal.
Bob you don't make laugh me. I and WolframAlpha we know as integration works.
BECAUSE:
Last edited by 21122012 (20130114 13:13:12) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #56 20130115 00:48:56
Re: The Structural Analysis  mathematics of the futurehi 21122012
I think I have worked out why you keep getting this wrong.
Note: I used r = kh. Wiki used h = kr. So our values of k are reciprocals of each other. Of course, this doesn't alter my calculus. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #57 20130115 07:43:13
Re: The Structural Analysis  mathematics of the future
Identical type of expressions  decide differently. On the ode of a variable the derivative undertakes, other letter registers.
Two functions, each function of two variables, in one option dependent are given, in the other  of the independent  is unclear on what function to consider a total derivative... Last edited by 21122012 (20130115 11:53:46) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #58 20130115 09:42:18
Re: The Structural Analysis  mathematics of the future
I do not understand you. OK? 2. Say u = pi r^2 = pi (kh)^2 What now? Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #59 20130115 11:55:51
Re: The Structural Analysis  mathematics of the futureHi bob! Last edited by 21122012 (20130115 11:57:04) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #60 20130115 15:45:36
Re: The Structural Analysis  mathematics of the futureHi Bob The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #61 20130115 16:09:38
Re: The Structural Analysis  mathematics of the future
Yes but it not I am the robot so translates. Last edited by 21122012 (20130115 16:13:21) "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #62 20130115 19:26:14
Re: The Structural Analysis  mathematics of the future
No. We still have not resolved post 22 You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #63 20130116 06:33:53
Re: The Structural Analysis  mathematics of the future
Hi bob General view of these two expressions the identical: You could teach me to that how to define the rule for integration. From where it is known that in one case one of variables for other variable is a constant and in other case they depend from each other. How to you it is prompted by a formula? Or each person establishes calculation rules itself voluntarily. After all answers turn out different. "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #64 20130116 06:57:45
Re: The Structural Analysis  mathematics of the future
Not to define the rules. Other before me have already done that. works for both. But the difference is that a cylinder has the same radius throughout its length => pi r^2 is constant, whereas for the cone the radius changes along the axis. pi r^2 is not constant. It varies with h So when you integrate you must change the 'r' into a function of 'h'. If you do not do this you calculate the volume of a cylinder not a cone. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #65 20130116 09:23:26
Re: The Structural Analysis  mathematics of the future
You didn't explain to me as it is possible using to receive ONE formula TWO various answers one of which is 3 times more than another. This is THREE volumes !!! So in Structural Analysis. Write as it looks at you: "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #66 20130116 10:24:29
Re: The Structural Analysis  mathematics of the futurehi 21122012 I will calculate the volume of the yellow slices for the cone. I will calculate the volume of the green slices for the cone. Note: For the cone I chose my values for R and H but they are related by a formula. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #67 20130116 12:14:20
Re: The Structural Analysis  mathematics of the futureI understand nothing. I ask you about integrals, and you write me algebra. You to me write how your cone has the same formula as the cylinder though is its part. And smaller part. All of you time act as the illusionist: you tell only that that is necessary for you but you don't answer my questions. "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! #68 20130116 19:17:55
Re: The Structural Analysis  mathematics of the futurehi 21122012,
When I am asked to explain something I go back to the basic theory. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #69 20130117 13:50:04
Re: The Structural Analysis  mathematics of the future
Hi bob! 2. How to evaluate a definite integral using the antiderivative of the integrand: where F is an antiderivative of f (i.e., F' = f). I think that on it the correct theory comes to an end. Nobody proved it and it doesn't make sense. Because: "The conditions imposed on functions, become a source of difficulties which will manage to be avoided only by means of new researches about the principles of integral calculus" Thomas Ioannes Stiltes. ... I made it! 