
Applications of Integration 15-21
Unlike in mid-point and trapezoidal rules, here n is required to be even because we are going to
approximate the curve with parabolic arcs where each arc passes through three consecutive points, i.e.
two of the subintervals, so if n is even we could approximate the whole curve with parabolas.
Now, let us compute the area bounded by the standard parabola y ax bx c
i
= + +
2
that passes
through three consecutive points ( , ( )),x f x
i i- -1 1
( , ( ))x f x
i i
and ( , ( ))x f x
i i+ +1 1
(refer Fig. 15.14), or
for our convenience we rewrite the points as ( , ( )),x h f x
i i
-
-1
( , ( ))x f x
i i
and ...