Estimation Error. The definite integral below can be computed using the Fundamental Theorem of Calculus. Calculate the actual value and then fill in the table with the given estimates and errors.

Question

Exact value =

In the table below, use the midpoint estimate with n rectangles, and use for the error column. Write the error in scientific notation using two significant digits.

What is the algebraic relationship between the number of rectangles and the size of the error?

Answer 1

So, use the midpoint definition of the integral approximation:

sum of i = 1 to n of (sqrt(2)-1)/n * f(1 + i*(sqrt(2)-1)/n - (sqrt(2)-1)/(2n)) where f is the integrand.

error is the difference of sum from different ns with the integral. (which is tan^-1(x))