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

1 Answer
Apr 17, 2018

#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#