Why is the trapezoidal integral better? I can see this on a rectangle/trazoid by rectangle/trapezoid basis, but if you integrate from a to b, every f_i gets evaluated twice, so the total sum should be the same, thus the same error of magnitude of the integral, right?
They are not the same. If delta(X )is evenly spaced, the difference between trapezoidal and forward difference is delta(X)/2*[f(b)-f(a)]. In the forward difference method, f(b) is not used so the information is lost
The best definition of "implicitly defined" ever!!! :))))
The gold is always best when kept hidden
Steve's lectures prove it
Why is the trapezoidal integral better? I can see this on a rectangle/trazoid by rectangle/trapezoid basis, but if you integrate from a to b, every f_i gets evaluated twice, so the total sum should be the same, thus the same error of magnitude of the integral, right?
They are not the same. If delta(X )is evenly spaced, the difference between trapezoidal and forward difference is delta(X)/2*[f(b)-f(a)]. In the forward difference method, f(b) is not used so the information is lost
Why the error is proportional to ∆x^2 I think it's proportional to just the value of ∆x