Question

A curve is passing through the points (1,2), (1.5,2.4), (2,2.7), (2.5,2.8), (3,3) then the area bounded by the curve, $X$-axis and $x=1,x=3$ using Simpson's rule is

• A. $5$
• B. $5.1$
• C. $5.2$
• D. $5.4$

Answer 1

The correct option is C $5.2$

$f\left(1\right)=2=y_0$
$f\left(1.5\right)=2.4=y_1$
$f\left(2\right)=2.7=y_2$
$f\left(2.5\right)=2.8=y_3$
$f\left(3\right)=3=y_4$
Now $h=\frac{b-a}{n}$
Here $h=0.5$
Hence
$Area$
$=\frac{h}{3}[y_0+2[y_2]+4[y_1+y_3]+y_4]$
$=\frac{0.5}{3}[2+2(2.7)+4(2.4+2.8)+3]$
$=\frac{0.5\times 31.2}{3}$
$=5.2$.