Finding "K" - Approximating the Error with Trapezoid and Midpoint Rule
Hello everyone. I'm trying to approximate the integral of cos(x^2) over the interval 0 to 1. I'm using the trapezoid and midpoint rule with 8 subintervals which is not a problem. However, I am to find the error bounds using the formulas given in the book and I am having trouble finding what "K" is. I need to find the second derivative of cos(x^2) and find the maximum value over the interval. I get the second derivative to be [(-4)*cos(x^2)*(x^2)] - [2sin(x^2)].
Over the interval 0 to 1, the maximum value of this equation I believe is 0, which would give me K = 0, but that can't be right because then the error bound would also be 0. Can someone please help me and tell me what I'm doing wrong to find K?