Use Newton's interpolating polynomial to approximate the function:
f (x) = e^ (-ax2) a = 1.1125
Construct approximation using the values f (x) at x= -2, -1, 0, 1, 2. Call this approximation N(x).
ii) Compute the value of the integral
accurate to 1 decimal place.
iii) Compute sufficient trapezium rule and the mid-point rule estimates for the integral
So that you may quote the integral's value to 1 decimal place. Hence compute the corresponding Simpson's rule estimate.
Is N(x) a good approximation to f(x)? Give a reason.
This has various problems regarding Newton's interpolating polynomial and Simpson's rule.