POV-Ray : Newsgroups : povray.advanced-users : car motion, calculus : Re: My own little question Server Time
30 Jul 2024 14:24:50 EDT (-0400)
  Re: My own little question  
From: Peter Popov
Date: 21 Jan 2000 18:39:04
Message: <Ge2IOPJcWleylnPyD2TmF+znoZsz@4ax.com>
On Fri, 21 Jan 2000 15:53:04 -0600, David Fontaine <dav### [at] faricynet>
wrote:

>So is the integral of sin(x) the area between the x-axis and sin(x) between x=0
>and x=x?

The integral of sin(x) (with respect to x :) ) is -cos(x). This is the
general form. In order to evaluate it for a particular range of x, or
in your case to find the area enclosed by the sine function and some
segment of the +x axis, you need to calculate the integral for that
range. Say the range is (a,b) then the integral evaluates to
-cos(b)-(-cos(a)) or cos(a)-cos(b). Of course this may give 0 as a
result and even though it represents an area this should not surprise
you because the part of the curve below the x axis is weighted
negatively.


Peter Popov
pet### [at] usanet
ICQ: 15002700


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