ABSTRACT
The ordinates x = a and x = b limit the area and such ordinate values are shown as limits. Hence
A = ∫ b
y dx (4)
(iv) Equating statements (2) and (4) gives:
Area A = limit δx→0
y δx = ∫ b
y dx
= ∫ b
f (x) dx
(v) If the area between a curve x = f ( y), the y-axis and ordinates y = p and y = q is required, then
area = ∫ q
p x dy
Thus, determining the area under a curve by integration merely involves evaluating a definite integral. There are several instances in engineering and science
determined. For example, the areas between limits of a:
velocity/time graph gives distance travelled, force/distance graph gives work done, voltage/current graph gives power, and so on.
