Approximate Integration (Estimating Error)

[SciGuy26]

Homework Statement

Found the approximation using Trapezoidal and Midpoint Formulas using 8 rectangles.
How do I estimate the error?

Homework Equations

$$\int^{1}_{0}$$ cos(x^2)dx

The Attempt at a Solution

Completely confused. I at first tried u-sub but later realized the error was far too great for my integration to be correct. Trig Identity is a no go here either.
I see in the text it wants be to take the derivative twice in order to use a formula to determine the upper bound or lower bound error...Should I differentiate? Ugh..too many questions. Please help

 

[Nino MMP]

. Trapezoidal Approximation: \frac{h}{2}[f(x_0)+2f(x_1)+2f(x_2)+...+2f(x_7)+f(x_8)]where h is the width of a single rectangle and x_i is the ith point in the interval [0,1]Midpoint Approximation:h\sum_{i=1}^{8}f(x_i)where h is the width of a single rectangle and x_i is the midpoint of the ith rectangle. Error: I am completely lost here. I believe I am supposed to differentiate twice but I am not sure how that applies here.