Section Summary: 6.1

  1. Definitions/Theorems

    The area A of the region bounded by the curves y=f(x), y=g(x), and the lines x=a and x=b, where f and g are continuous and tex2html_wrap_inline123 for all x in [a,b], is

    displaymath103

    The area A between the curves y=f(x), y=g(x), and the lines x=a and x=b is

    displaymath104

  2. Properties/Tricks/Hints/Etc.

    It's sometimes necessary to find the area A between the curves x=f(y), x=g(y), and the lines y=c and y=d, with tex2html_wrap_inline149 : this is

    displaymath105

    No great shakes, here: just switch the roles of x and y in the equations, and you can do them using the ``x'' formulas; but it's a minor convenience to be flexible enough to skip the step, and go directly to integrating along the y axis.

  3. Summary

    There's nothing particularly remarkable in this section: it simply generalizes the problem of finding areas under functions to the problem of finding areas between functions.

Problems:

Problems, pp. 376-378, #2, 3, 9, 20, 35, 40, 41, 44

At seats: #1, 4, 40





LONG ANDREW E
Tue Apr 3 11:23:38 EDT 2001