If x is given as a function of y, say x = g(y), then (Figure N7–3) the
subdivisions are made along the y-axis, and the area bounded by the y-axis, the
curve, and the horizontal lines y = a and y = b is given exactly by
.
See Questions 3 and 13 in the Practice Exercises.Figure N7–3A1. Area Between Curves
To find the area between curves (Figure N7–4), we first find where they intersect
and then write the area of a typical element for each region between the points of
intersection. For the total area bounded by the curves y = f (x) and y = g(x)
between x = a and x = e, we see that, if they intersect at [c,d], the total area is
given exactly by .
See Questions 4, 6, 7, and 9 in the Practice Exercises.