There's really nothing too new here: just instead of calculating the area between a curve (the graph of the function given by f(x)) and the x-axis (the graph of the function g(x)=0), we compute the area between two arbitrary curves, given by the graphs of f(x) and g(x):
If we're computing area -- real, honest-to-goodness, positive area -- then we have to make sure that we know which function's graph is "on top". In effect, we want to compute
but the absolute values are a pain (not for your calculator, however!); when we're doing these "by hand", we have to figure out the regions for which f(x)>g(x), and vice versa.
Examples:
#3, p. 306
#7, p. 306
#52, p. 308
One of the interesting twists in this section is integrating along the
y-axis. Actually, we could just swap variables x and y,
and we'd be back to integrating along the x-axis, but we should be more
dexterous than that...
Examples:
#20, p. 307
#27, p. 307
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