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You are not logged in. #1 20060123 18:22:06
fundamental theorem of calculus part 2Just read about this today. It stated that every continuous function has an antiderivative. My book then trailed off on something about integreting with a constant as the lower limit of integration. In the end I couldn't see there point, and they then simply said "we state the theorem without proof:" A logarithm is just a misspelled algorithm. #2 20060124 02:00:54
Re: fundamental theorem of calculus part 2Correct me if I'm wrong, but isn't it this? I think you're thinking of e^{x²}. Anyway, every function can be integrated, it's just that not all of them can be integrated algebraically. If you wanted to find ∫e^{x²}dx, you'd need to take each and every real value of x and work out the integral at that point using numerical methods. I'd advise telling a computer to do it. Why did the vector cross the road? It wanted to be normal. #3 20060124 02:27:31
Re: fundamental theorem of calculus part 2
If you mean e^x^2, then you're going to love this one. There is an antiderivative of e^x^2. But we can't integrate it. There is a function of it's antiderivative, but it was a function that was unknown until we were investigating the antiderivative of e^x^2. Here is an example you will understand: That is the defintion of ln(x). The same thing happens when you take the integral of e^x^2. The function is defined by that integral. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 