Daniel0 Posted January 31, 2009 Share Posted January 31, 2009 Okay so I'm kind of stuck (yes, homework; no, not php). I have a second degree polynomial f(x)=ax2+bx+c where a=-5 and f(x)=-3 and f(x)=-2. I'm asked to figure out what [tex]\int_{-2}^{-3} f(x)dx[/tex] is. How the hell am I supposed to solve that? Quote Link to comment Share on other sites More sharing options...
corbin Posted February 1, 2009 Share Posted February 1, 2009 Oh my God am I glad I'm not in what ever math class you're in. Quote Link to comment Share on other sites More sharing options...
genericnumber1 Posted February 2, 2009 Share Posted February 2, 2009 Heh, I read your question and thought "it's just the fundamental theorem of calculus..." until I realized the information given. "a second degree polynomial f(x)=ax2+bx+c where a=-5 and f(x)=-3 and f(x)=-2." Wha? Maybe if they gave you f'(x) and/or f''(x)... Tell us when you find out the method of solving for b and c, I'm curious Quote Link to comment Share on other sites More sharing options...
Mchl Posted February 2, 2009 Share Posted February 2, 2009 This is strange task... I mean... what are f(x)=-3 and f(x)=-2 supposed to mean? Quote Link to comment Share on other sites More sharing options...
Daniel0 Posted February 2, 2009 Author Share Posted February 2, 2009 This is strange task... I mean... what are f(x)=-3 and f(x)=-2 supposed to mean? It was just the way I decided to write that the roots of f(x) are -3 and -2. It wasn't worded that way in the assignment. That's false of course - no function can have two outputs. I meant to say that -3 and -2 satisfies f(x)=0. Anyway, it turned out to be rather simple. I forgot that for a second degree polynomial where x1 and x2 are roots it's true that f(x)=ax2+bx+c=a(x-x1)(x-x2) so with that information it's just a matter of integrating -5(x+3)(x+2). Quote Link to comment Share on other sites More sharing options...
Mchl Posted February 2, 2009 Share Posted February 2, 2009 Lol Next time write f(-3) = 0, f(-2) = 0 Quote Link to comment Share on other sites More sharing options...
Daniel0 Posted February 2, 2009 Author Share Posted February 2, 2009 Could do that too Quote Link to comment Share on other sites More sharing options...
corbin Posted February 2, 2009 Share Posted February 2, 2009 *runs off to google "integrals"* Wooo for "pre-calc w/ trig" lol. Quote Link to comment Share on other sites More sharing options...
Daniel0 Posted February 2, 2009 Author Share Posted February 2, 2009 It's not too difficult. The book tricked me though. The question mentioned above wasn't really about calculus even though it was along with a lot of other questions about integrals, it was checking that I knew WTF factorization was, which I of course had forgotten. Quote Link to comment Share on other sites More sharing options...
genericnumber1 Posted February 2, 2009 Share Posted February 2, 2009 I hate when they throw easy questions in with all of the hard questions, especially when the easy questions look harder than the rest... [tex]\int_{\frac{7\pi}{2}}^{\frac{7\pi}{2}} 17x^2-ln(83)\frac{16}{x^2+17}+e^9^x dx[/tex] My professor LOVED to do that kind of shit to us ^ Quote Link to comment Share on other sites More sharing options...
Daniel0 Posted February 2, 2009 Author Share Posted February 2, 2009 Do they allow you to solve it using CAS? Quote Link to comment Share on other sites More sharing options...
genericnumber1 Posted February 2, 2009 Share Posted February 2, 2009 We use Matlab for some problems, but we can't use it (or calculators) for normal homework, tests, or quizzes. Quote Link to comment Share on other sites More sharing options...
Daniel0 Posted February 2, 2009 Author Share Posted February 2, 2009 Ah. At our written exams we have 1 hour without aids and 4 hours with all aids excluding communication with other people (thus also excluding internet). At oral exams they mostly just want us to be able to do proofs and possibly apply knowledge about a particular area of mathematics. Regular homework is usually also with aids. Quote Link to comment Share on other sites More sharing options...
genericnumber1 Posted February 2, 2009 Share Posted February 2, 2009 But I'd guess your problems are much more complex than ours... they don't expect us to factor ninth degree polynomials or anything insane like that by hand. I suppose it's a tradeoff. Quote Link to comment Share on other sites More sharing options...
Daniel0 Posted February 2, 2009 Author Share Posted February 2, 2009 The following is an example of a one of the tasks that might be at an exam at B level math (out of A, B, C, where A is highest and C is lowest): A company manufactures a product. The costs C(x) of manufacturing said product at x tons per week is given by: C(x)=x3-30x2+500x+30 where C(x) is expressed in a currency that is irrelevant in this matter. The manufactured amount of products can be sold at a fixed price of 308/ton. Determine the amount of tons the company must manufacture per week in order to maximize profit. The figure shows the end of a parabola shaped hall. a) Insert the figure on a suitable coordinate system. b) Calculate the area of the figure. Dunno if that's more complex than whatever you're given. The curriculum ranges over multiple subjects such as functions and graphs, statistics, trigonometry, differentiation, integration, etc. Quote Link to comment Share on other sites More sharing options...
genericnumber1 Posted February 2, 2009 Share Posted February 2, 2009 Ah, so you're in a kind of mixed-math class? I'm in an "Engineering Math" class, (basically, differentiation and integration calculus) whose problems (so far) are consisting of determining volumes of solids through integration, calculating work, etc. Probably much easier than the kind of stuff you have to deal with. Something like... A wedge is cut out of a circular cylinder of radius 4 by two planes. One plane is perpendicular to the axis of the cylinder. The other intersects the first at an angle of 30 degrees along a diameter of the cylinder. Find the volume of the wedge. Quote Link to comment Share on other sites More sharing options...
Daniel0 Posted February 3, 2009 Author Share Posted February 3, 2009 Yes, I'm in this kind of school. I think in Denmark that math courses aren't divided into specialized topics until university. I mentioned previously that math in my kind of school are split in A/B/C and that I have B. I'm going to study computer science and for that I'll need A which, in addition to everything C and B encompass, covers (by looking at the TOC for the textbook in the series we use, but for A level) vectors and analytical geometry, infinitesimals, and differential equations. For computer science on the university it appears that in addition to that, the courses "discrete mathematical structures" and "linear algebra" are required. Then there are of course even more advanced math depending on what courses you choose (e.g. cryptology or stuff dealing with images or sound). Quote Link to comment Share on other sites More sharing options...
genericnumber1 Posted February 3, 2009 Share Posted February 3, 2009 Yeah, it's the same deal with my college.. So-called "Engineering Math (calculus) 1, 2 and 3", Linear Algebra and statistics. The computer science department here has their own Discrete Structures course though, so thankfully I can learn it in the context I will use it. One more math class and computer science majors can easily minor in math here. And hey, Denmark, a country that produces someone like Stroustrup should be a great place to take computer science. Quote Link to comment Share on other sites More sharing options...
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