Question

use the simpsons rule with n=10, arc length y=^3√x, for 1<=x<6

Answer 1

fix your equation first

Answer 2

I think she means y = ∛x

Answer 3

y = ∛x for 1 is less then or equal to x and x is less then 6

Answer 4

I assume that you know the formula ....
in case you don't, here is the method
http://www.mathwords.com/s/simpsons_rule.htm

∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9

interval = (6-1)/10 = 1/2

then we have
(5/9)[ f(1) + 4f(1.5) + 2f(2) + 4f(2.5) + 2f(3) + 4f(3.5) + 2f(4) + 4f(4.5) + 2f(5) + 4f(5.5) + f(6) ]
= (5/9)[ 1 + 4.5789 + 2.5198 + ... + 7.0607 + 1.81712 ]

I will let you do the rest of the button pushing.

Answer 5

∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9
should be
∆x = (6-1)/10 = 5/3 , so ∆x/3 = 5/30 = 1/6

and the 5/3 in front of the big brackets should be 5/30 or 1/6

Answer 6

aprox 10.2688 thank you so much