Writing Assignment #1
On clean paper, legibly print or write, in clear and concise English, a description of the development of the definite integral over a segment [a, b]. You may use a specific function or a general function, f. Your description should be logically organized, didactic, and sufficient that any individual with pre-calculus training could follow it (you do not have to explain what a derivative is). It should also include the following:
- a basic statement of the problem (curve defined by y = f(x) on an interval [a, b];
- a list of conditions necessary for the Riemann integral to exist;
- an explanation of the role that partitions, minimums or maximums and limits play in the integral;
- the role that the fundamental theorem of calculus plays in evaluating definite integrals.
*** Note that you can write on the Riemann integral or the Darboux integral (whichever one you are more familiar with).
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