Question

Using Simpson's rule, by taking 4 equal parts,the value of ${\int }_1^5(2x-1)dx$ is?

• A. $22$
• B. $20.7$
• C. $20$
• D. $19.7$

Answer 1

The correct option is C $20$

Here $f\left(x\right)=2x-1$ and $a=1,b=5$
$f\left(1\right)=1,f\left(3\right)=5,f\left(5\right)=9$
Now ${\int }_1^5(2x-1)dx=\frac{4}{3}\left(f\right(1)+f(3)+f(5\left)\right)$
$I=20$