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And that, in a nutshell, is the difference between scientists and engineers.
at any rate, a simpler formula will be quicker to evaluate by the computer. (so we could all save a few billionths of a second)
You are correct ryos, it wouldn't really matter if this problem was to be solved by a computer. The two answers are indeed equal. I was thinking however about the scenario in which the result was going to be an integral (pun not intended) part of one's work. Remembering and applying their formula would be much harder than would be necessary. I, for one, had until now believed that such programs simplified their answers for our convenience.
As my Calc teacher once said, "Machines sometimes give us some interesting answers..."
Is the Mathmatica Integrator broken or that limited?
If you guys want to laugh, Mathmatica's online integrator gives;
not all the time. But on occasions were it happens, best to be prepared.
Yeah, mikau, I have never had any trouble with doing that. I don't recall ever being taught to do it specifically, but like I said, I haven't seen it ever getting me into trouble before.
Very true. Nice observation.
Yes, mikau, you can always replace the u with what you substituted it for after you are done integrating. I think it's just a matter of preference. You either do what I did or you change the limits of integration. I just think it is usually easier to do it the way I did because I already know what u equals. If you change the limits of integration then you have to solve for the values of u.
wow! Many thanks irspow! I was stuck on that one for weeks!
It's just another substitution...
hmm... are you sure its legal to replace x with expressions containing u after differentiating? I don't see why it wouldn't be but there are a lot of things that I think should work but don't. :-/
Let u = x^(1/3)
lol. I do agree. I mean I use a calculator to add subtract multiply and divide when I can't do it in my head, rather then using long division or multiplication.