[plt-scheme] HtDP Exercise 23.4.1

Thanks Dan.  Looks like the original formatting from HtDP didn't carry over
from my cut-and-paste.  Still don't really understand how this relates to
the question of computing the "area of each trapezoid," though.

Cheers,
Dave

On Mon, Feb 9, 2009 at 3:32 PM, <danprager at optusnet.com.au> wrote:

>
> > divide the interval into two parts: [a,(a + b/2)] and [(a + b/2),b];
>
> Try: [a,(a+b)/2 and [(a+b)/2, b]
>
> (a+b)/2 is the mid-point between a and b: (a + b/2) ain't.
>
> -- Dan
>
>
>
> > dave yrueta <dyrueta at gmail.com> wrote:
> >
> > Hi All --
> >
> > Am sending out a message in a virtual bottle for help with HtDP
> > exercise 23.4.1, reproduced below:
> >
> > A general integration function must consume three inputs: a, b, and
> > the function f. The fourth part, the x axis, is implied. This suggests
> > the following contract:
> >
> > ;; integrate : (number  ->  number) number number  ->  number
> > ;; to compute the area under the graph of f between a and b
> > (define (integrate f a b) ...)
> > Kepler suggested one simple integration method. It consists of three
> > steps:
> >
> > divide the interval into two parts: [a,(a + b/2)] and [(a + b/2),b];
> >
> > compute the area of each trapezoid; and
> >
> > add the two areas to get an estimate at the integral.
> >
> > Exercise 23.4.1.   Develop the function integrate-kepler. It computes
> > the area under some the graph of some function f between left and
> > right using Kepler's rule.
> >
> > Specifically, I'm stuck at the "create examples" part of the design
> > recipe, because I don't understand the "integration method" outlined
> > by the exercise.
> >
> > First, what does it mean to "divide the interval into two parts?"
> > Suppose I substitute values for variables a and b (a=3 and b=6).  I
> > end up with a pair of values: [3, 6] and [6, 6].  Are these x,y
> > coordinates for points on a graph?  If so, how do they relate to the
> > second step of the integration method, which is to determine the area
> > for "each trapezoid?"
> >
> > I know the area for a trapezoid = a (b1 + b2 /2) where a is the
> > altitude, and b1 and b2 are the length of the two bases.  My problem
> > is deriving values for a, b1 and b2 from the integrate-kepler function
> > arguments.
> >
> > Finally, I have no idea how argument f, the line function, fits into
> > all this.  I don't even know what a function for a line looks like (y
> > = x + 10?)
> >
> > HtDP supplies an illustration to help visualize the problem (http://
> > www.htdp.org/2003-09-26/Book/curriculum-Z-H-29.html#node_sec_23.4).  I
> > haven't the faintest idea how to interpret it:
> >
> > I'm sure someone even casually acquainted with basic calculus could
> > solve this problem easily.  Unfortunately, I'm relatively math-
> > illiterate, so figuring out how all the parts fit together has eluded
> > me.  I did manage to solve the other mathematical examples which
> > appeared earlier in the chapter because the mechanics of determining
> > the solution appeared clear to me.  Not so here. I'm hoping that if
> > someone can help me formulate some examples, I'd be on my way.
> >
> > Thanks!
> >
> > Dave Yrueta
> > _________________________________________________
> >   For list-related administrative tasks:
> >   http://list.cs.brown.edu/mailman/listinfo/plt-scheme
>
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