Thread: Trapezoid Rule - Approximating the Error with Integrals

Hey everyone. I posted something similar a while back, but I just still seem to be having major problems finding the "K" while doing the trapezoid rule error bound approximation. I understand that I find the second derivative of the equation, find at what point on the interval (absolute value of course) it attains its max value, and then plug in that X into the second derivative equation to give me my K. For whatever reason though I just always do it wrong. For example, could someone walk me through this problem? Thank you!

Sqrt[ 1 + x^4 ] from 0 to 1. Approximate the error using n=10 sub intervals and the Trapezoid Rule for error bounds.

Anyone? I'm honestly not just trying to figure out a homework problem or something. I just can never seem to find K. For this problem, I got the second derivative to be:

f'' = [ (2x^2)(x^4 + 3) ] / [ (x^4 +1)^(3/2) ]

The interval is from 0 to 1, so my understanding is that since the max value (I think) occurs at x=1, I plug in 1 for x and get my K. But that is not working. Any ideas about this problem or about finding K in general?