Question

Using Trapezoidal rule, by dividing the interval $[0,4]$ into 4 equal parts, the approximate value of ${\int }_0^4(x^2+1)$ is equal to

• A. $25$
• B. $26$
• C. $27$
• D. $28$

Answer 1

The correct option is B $26$

Here $h=\frac{4-0}{4}=1$
We have

$x$	$0$	$1$	$2$	$3$	$4$
$x^2+1$	$1$	$2$	$5$	$10$	$17$
	$y_0$	$y_1$	$y_2$	$y_3$	$y_4$

By trapezoidal rule,
${\int }_0^4(x^2+1)dx$
$=\frac{h}{2}[(y_0+y_4)+2(y_1+y_2+y_3)]$
$=\frac{1}{2}[(1+17)+2(2+5+10)]$
$=\frac{1}{2}[18+34]=\frac{52}{2}=26$