Question

Dividing the interval $[0,6]$ into $6$ equal parts and by using trapezoidal rule the value of $\underset{0}{\overset{6}{\int }}{x}^{3}dx$ is approximately :

• A. 330
• B. 331
• C. 332
• D. 333

Answer 1

Answer: (D)

$x$	0	1	2	3	4	5	6
$f(x)$	0	1	8	27	64	125	216

By trapezoidal rule
$\underset{0}{\overset{6}{\int }}{x}^{3}dx=\frac{h}{2}\{y_0+y_6+2(y_1+y_2+y_3+y_4+y_5)\}$
$=\frac{1}{2}\{0+216+2(1+8+27+64+125)\}$
$=\frac{1}{2}\{216+450\}=\frac{666}{2}$
$=333$