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        riddles >> medium >> integral
        
(Message started by: tony123 on Aug 2^nd, 2007, 1:46am)

Title: integral
Post by tony123 on Aug 2^nd, 2007, 1:46am

find the folowing integral

1/(4 + 5 ( cos x )^2 ) dx

Title: Re: integral
Post by ThudanBlunder on Aug 2^nd, 2007, 4:17am

I think I recognise this integral from way back, but can't remember the substitution.
Anyway, it gives [hide](1/6)tan^-1[(2tanx)/3] + c[/hide]

Title: Re: integral
Post by pex on Aug 23^rd, 2007, 8:14am

on 08/02/07 at 04:17:14, ThudanBlunder wrote:

I think I recognise this integral from way back, but can't remember the substitution.
Anyway, it gives [hide](1/6)tan^-1[(2tanx)/3] + c[/hide]

It isn't all that difficult - see attachment.

Title: Re: integral
Post by srn347 on Sep 1^st, 2007, 10:59pm

Even though I understand integrals, I don't understand the dx whatever representation. It is the integral of what with respect to what?

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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
http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/int.gif^b_a 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
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