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wu :: forums    riddles    medium (Moderators: Eigenray, Grimbal, SMQ, ThudnBlunder, william wu, towr, Icarus)    integral « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: integral  (Read 531 times) tony123 Junior Member     Posts: 61 integral   « on: Aug 2nd, 2007, 1:46am » Quote Modify find the folowing integral     1/(4 + 5 ( cos x )^2 ) dx IP Logged ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: integral   « Reply #1 on: Aug 2nd, 2007, 4:17am » Quote Modify I think I recognise this integral from way back, but can't remember the substitution.   Anyway, it gives (1/6)tan-1[(2tanx)/3] + c « Last Edit: Aug 2nd, 2007, 6:30am by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. pex Uberpuzzler     Gender: Posts: 880 Re: integral   Cosine_Integral.pdf « Reply #2 on: Aug 23rd, 2007, 8:14am » Quote Modify on Aug 2nd, 2007, 4:17am, ThudanBlunder wrote: I think I recognise this integral from way back, but can't remember the substitution.   Anyway, it gives (1/6)tan-1[(2tanx)/3] + c It isn't all that difficult - see attachment. IP Logged srn437 Newbie the dark lord rises again....     Posts: 1 Re: integral   « Reply #3 on: Sep 1st, 2007, 10:59pm » Quote Modify Even though I understand integrals, I don't understand the dx whatever representation. It is the integral of what with respect to what?       // ------ I've cleaned up the thread below, but I don't what to bring this thread back to the top. So I'll answer the question here:   An integral is typically written as      ba f(x) dx where f(x) is a function, and the integral is with respect to x   dx represent a very,very small length a long the x direction. By dividing the range [a..b] into very small pieces, and multiplying the length of each piece with the average height of the function at that point, you get an approximation of the area under the function on the range [a..b], i.e. the integral. As dx goes to 0, the approximation becomes exact (or just about. Read up on Riemann sums and integrals if you want a more rigorous account)   --towr ------ // « Last Edit: Sep 14th, 2007, 4:58am by towr » IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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