
15-26 Calculus – Differentiation and Integration
By the Simpson’s rule, we have
y dx
h
y y y y y y y
0
60
0 6 2 4 1 3 5
3
2 4
10
3
0 0212765 0 0
∫
= + + + + + +
[ ]
=
+
( ) ( ) ( )
( . . 2263157 2 0 0185185 0 0163934
4 0 0172413 0 0153846 0 01
) ( . . )
( . . .
+ +
+ + + 992307
1 082808
)
. .
=
Hence, the time taken to travel 60 ft is 1.064.
15.1.3 Length of a Plane Curve
Let y = f(x) be a continuous differentiable plane curve defined on [a, b] as shown in Fig. 15.15. We
shall derive a formula for the length of the curve, say L, on the interval [a, b].
For this, we divide the interval [a, b] into n subintervals
[ , ], [ , ], , [ , ], , [ , ],x x x x x x x