> 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 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