Question

Use simpson's method to approximate integral 0 to 8(x^2-x+3)dx with 8 such-intervals.

Answer 1

$simpson's$ $rule$ ,

$y = x^{2}-x+3$

$integral$

$a =0$

$b =8$

$interval$

$n =8$

$Area = \int_{a}^{b} f(x)dx$

$=\frac{\triangle x}{3} (y_{0}+4y_{1}+2y_{2}+4y_{3}+2y_{4}....+4y_{n-1}+y_{n})$

$where \triangle x = \frac{b-a}{n}$

$y_{0} = 0-0+3 =3$

$y_{1} = 3$

$y_{2} = 5$

$y_{3} = 9$

$y_{4} = 15$

$y_{5} = 23$

$y_{6} = 33$

$y_{7} = 45$

$y_{8} = 59$

$\triangle x = \frac{8-0}{8}$

$\triangle x =1$

$area =\frac{1}{3} (3+4\times3+2\times5+4\times 9+2\times15+4\times23+2\times33+4\times45+59)$

 $area = 162.67$