Question

Using Trapezoidal rule, by taking $3$ equal inter- vals, the value of ${\int }_1^{4}3x^{2}dx$ is?

• A. $24.5$
• B. $34.5$
• C. $64.5$
• D. $74.5$

Answer 1

Answer: (C)

$64.5$

$h=\frac{b-a}{n}$
Here $n=3$ $b=4$ and $a=1$
Therefore
$h=1$.
$f\left(1\right)=3=y_0$
$f\left(2\right)=12=y_1$
$f\left(3\right)=27=y_2$
$f\left(4\right)=48=y_3$.
Using trapezoidal rule we get
$△=\frac{h}{2}[y_0+2[y_1+y_2]+y_3]$
$=\frac{1}{2}[3+2[12+27]+48]$
$=64.5$