Section Summary: 5.2 - The definite integral

  1. Definitions

  2. Theorems

  3. Properties/Tricks/Hints/Etc.

  4. Summary

    Whew! There's a lot going on in this section. The main idea is that we generalize from area to the integral, which is a way of defining the net area (i.e., some area is considered positive, and some negative; the integral is the sum of both parts for any function). Regions trapped between the curve of f and the x-axis, but above the x-axis, are considered positive in area; those below the x-axis are considered negative.

    The integral of a function is a linear operation - that is, if

    displaymath201

    is integration (taking a function f and returning a number v), then if I(f) = v and I(g) = w we have that

    displaymath202

    We are introduced to the midpoint rule, which is an improvement on either the right or left endpoint rules. While subintervals are generally of fixed width tex2html_wrap_inline238 , it is not necessarily so, and may sometimes be more convenient to use variable sized rectangles.

Problems:

Problems, pp. 334-336, #1-3, 6, 30, 31, 40, 46, 49, 64

At seats/the board: #5, 7 (Argh!), 32, 47, 14





LONG ANDREW E
Mon Mar 26 11:29:44 EST 2001