Question

A curve is drawn to pass through the following points

x :1	1.5	2	2.5	3	3.5	4
y: 2	2.4	2.7	2.8	3	2.6	2.1

Using Simpsons rule the approximate area bounded by the curve, the X-axis and the lines $x=1$ and $x=4$ is

• A. 6.78 sq. units
• B. 7.78 sq. units
• C. 7.73 sq. units
• D. 7.68 sq. units

Answer 1

Answer: (B)

7.78 sq. units

The approximate area $\frac{h}{3}[S+2S_o+4S_e]$
$=\frac{0.5}{3}[4.1+2\left(5.7\right)+4\left(7.8\right)]$
$=\frac{5}{30}[4.1+11.4+31.2]=\frac{5}{30}\left(46.7\right)=7.78$