Question

By Simpson's $\left(\frac{1}{3}\right)$rd rule, the approximate value of ${\int }_2^4(1+x^3)dx$, taking $n=2$, is.

• A. $62$
• B. $61$
• C. $60$
• D. $59$

Answer 1

The correct option is A $62$

Here, $h=\frac{4-2}{2}=1$
We have,

$x$	$2$	$3$	$4$
$1+x^3$	$9$	$28$	$65$
	$y_0$	$y_1$	$y_2$

By Simpson's rule
${\int }_2^4(x^3+1)dx=\frac{1}{3}\left[\right(9+65)+4(28\left)\right]$
$=\frac{1}{3}[74+112]=\frac{186}{3}=62$