find the Errors for $ \ n=2 \ $ and $ \ n=20 \ $

Question

Let $ \ I=\large \int_a^b f(x) dx=7.621372 \ $ and let the trapezoidal approximation for $ \ n=2 \ $ is given by $ I_T=\int_a^b f(x) dx \approx 7.362011 \ $ . Then find the Errors for $ \ n=2 \ $ and $ \ n=20 \ $

Answer:

$n $ = number of sub-intervals

For $ n=2 \ $ the Error is given by $ E=|I-I_T|=|7.621372-7.362011|=0.259361 \ $

But how to find the Error for $ \ n=20 \ $ ?

Help me out

Answer 1

As the error is $O(h^2)=O(n^{-2})$, your best guess is to divide by $10^2=100$ to get a probable error for $n=20$ of $0.0026$.