Can someone explain to me what theoretical error bound means in the context of this question?

[dire egret]

any assistance would be much appreciated

[fallow tartan]

so you use the function K(b-a)³/12n² where K is the largest possible absolute value of the second derivative of the function you're integrating

and R_5 is the Riemann summation where n=5

so K(15)³/12(5)² which evaluates to 11.25K

second derivative of (x²+1)^-1 is 8x²((x²+1)^-3)-2((x²+1)^-2)

and that maxes at 0,-1,1

you can do the rest

@dire egret

largest absolute value is 2

[dire egret]

Thanks man

[olive cobalt]

@dire egret has given 1 rep to @fallow tartan

[dire egret]

I’m sorry to bother you, I just wanted to ask, do you think I did it correctly?

[fallow tartan]

answer looks fine

[dire egret]

thanks man