Question

Using Trapezoidal rule, by taking $4$ equal intervals,

the value of ${\int }_1^5(2x+1)dx$ is?

• A. $5$
• B. $8$
• C. $28$
• D. $28.2$

Answer 1

The correct option is C $28$

$h=\frac{b-a}{n}$
Here $n=4$ $b=5$ and $a=1$
Therefore
$h=1$.
$f\left(1\right)=3=y_0$
$f\left(2\right)=5=y_1$
$f\left(3\right)=7=y_2$
$f\left(4\right)=9=y_3$
$f\left(5\right)=11=y_4$.
Using trapezoidal rule we get
$△=\frac{h}{2}[y_0+2[y_1+y_2+y_3]+y_4]$
$=\frac{1}{2}[3+2[5+7+9]+11]$
$=28$.