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You are not logged in. #1 20130723 01:32:39
An Integral and the ComputerCan anyone tell how to find the value of the following integral upto four significant digits with the help of a computer but not a readymade CAS? My first question is : Does cos(x)^100 mean (cos (x))^100 or (cos (x^100)? Last edited by Agnishom (20130723 01:32:54) 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #2 20130723 02:40:56
Re: An Integral and the ComputerHi Agnishom; You can integrate mostly any integrand using the methods of numerical analysis and a computer. Numerical methods can do way more integrations than even those wonderful analytical methods that they bore kids with. 1) You take a look always at the geometry of the problem. This is done by plotting. What do you observe? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20130723 02:54:17
Re: An Integral and the ComputerHow do you find the area of that numerically? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #4 20130723 03:02:32
Re: An Integral and the ComputerHey, I just got an idea! 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #5 20130723 03:03:22
Re: An Integral and the ComputerYou will need to use of one of the standard ways. Romberg, Gaussian, Newton Cotes, Simpsons, Trapezoidal, Euler Mclaurin Summation etc. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #6 20130723 03:11:43
Re: An Integral and the Computer
What are these? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #7 20130723 03:17:55
Re: An Integral and the ComputerThat is the basic method that you will be using for all of the above methods. But you will still have to do the function evaluations... This was not done by M but by a little routine I wrote for M. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #8 20130723 13:35:24
Re: An Integral and the Computer
Do you mean a CAS? That I have already done, with another M  Maxima. I am getting: Please explain me these:
Last edited by Agnishom (20130723 13:37:47) 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #9 20130723 17:32:45
Re: An Integral and the ComputerYes, a CAS is a great tool.
In this case I did not mean using the integrate command. I meant writing a numerical integration routine using one of the above algorithms. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #10 20130723 18:39:35
Re: An Integral and the ComputerI think so 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #11 20130723 18:44:07
Re: An Integral and the ComputerThe simplest is the Trapezoid rule. Instead of stuffing rectangles, it is intuitively obvious that stuffing trapezoids will yield better results. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #12 20130723 18:50:33
Re: An Integral and the ComputerI agree, so... 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #13 20130723 18:57:55
Re: An Integral and the ComputerThat means less stuffing of trapezoids compared to rectangles. That means less computation which means faster convergence, more numerical stability and happier computers. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #14 20130723 19:35:41
Re: An Integral and the ComputerYes, is it something related to simpson? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #15 20130723 19:37:52
Re: An Integral and the ComputerSimpsons rule is the next thing. It should have replaced the trapezoidal rule but the trapezoidal rule is used inside Romberg integration so it is still around. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #16 20130723 19:39:27
Re: An Integral and the ComputerOk, please put the trap. Rule in action 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #17 20130723 19:55:06
Re: An Integral and the ComputerThere are many variations of it but here is the crudest one just for illustration purposes: Now for your problem we have: Now using A) we get: Can you compute that? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #18 20130723 20:12:18
Re: An Integral and the ComputerAre you telling me to plug a and b as 0 and pi/4? Last edited by Agnishom (20130723 22:54:22) 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #19 20130723 20:13:15
Re: An Integral and the ComputerYes, that is correct. But I would like you to do it on your own. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #20 20130723 20:15:55
Re: An Integral and the ComputerOk, but after a while: I am not feeling well right now. 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #21 20130723 20:19:16
Re: An Integral and the ComputerOkay, I will fill it in for you. You just relax. That is not very accurate is it? Why is it not? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #22 20130723 22:46:47
Re: An Integral and the ComputerI am sorry. I was feeling very weak then, I have a stomach upset. 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #23 20130723 22:55:25
Re: An Integral and the ComputerThat is okay, I hope you are feeling better. If not then get some rest and we can continue later or tomorrow. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #24 20130723 23:00:38
Re: An Integral and the Computern is the number of intervals or something like that I suppose? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #25 20130723 23:13:35
Re: An Integral and the ComputerHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 