Question

A(1,4), B(1.5, 5) and C(2,6) are three points on the curve defined by $f\left(x\right)$, Numerical integration is carried out using both trapezoidal rule and Simpson's rule with in limits $x=1$ and $x=2$ for the curve, the difference between the two results will be __

• A. 0

Answer 1

The correct option is A 0

x	1	1.5	2
y	4	5	6
	$y_0$	$y_1$	$y_z$

By trapezoidal rule,
${\int }_1^{2}f\left(x\right)dx=\frac{h}{2}\left[\right(y_0+y_2)+2y_1]=\frac{o.5}{2}\left[\right(4+6)+2(5\left)\right]=5$

By simpson's rule,

${\int }_1^{2}f\left(x\right)dx=\frac{h}{3}\left[\right(y_0+y_2)+4y_1]=\frac{o.5}{2}\left[\right(4+6)+4(5\left)\right]=5$

The difference between the two results will be zero