Question

The definite integral ${\int }_1^6{x}^{3}dx$ is evaluated using trapezoidal rule with a step size of 1. The correct answer is

• A. 252
• B. 396
• C. 227.5
• D. 332.5

Answer 1

The correct option is D 332.5

x	1	2	3	4	5	6
y=f(x)	1	8	27	64	125	216
$y_n$	$y_0$	$y_1$	$y_2$	$y_3$	$y_4$	$y_5$

$I={\int }_1^6{x}^{3}dx=\frac{h}{2}\left[\right(y_0+y_5)+2y_1+2y_2+2y_3+2y_4]$
$=\frac{1}{2}\left[\right(1+216)+1(8+27+64+125\left)\right]$
$=\frac{1}{2}[217+448]=332.5$