Question

Calculate the approximate value of `int_0^6x^3 dx` by taking 6 subintervals of equal length and applying Simpson's rule?

Answer 1

`int_0^6x^3dx~~324`

Explanation:

Simpson's rule says that `int_b^af(x)dx` can be approximated by `h/3[y_0+y_n+4y_(n="odd")+2y_(n="even")`

`h=(b-a)/n=(6-0)/6=6/6=1`

`int_0^6x^3dx~~1/3[0+216+4(1+27+125)+2(8+64)]=[216+4(153)+2(72)]/3=[216+612+144]=972/3=324`