A class wants to approximate the length of a twice-differentiable curve on using…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

A class wants to approximate the length of a twice-differentiable curve on

[p,q]

using

n

equally spaced subintervals where

n

is even. Which of the following numerical rules is most likely to yield the smallest absolute error for the same

n

? (a)

\text{Trapezoidal Rule}

(b)

\text{Midpoint Rule}

(c)

\text{Simpson's Rule}

(d)

\text{Left Riemann Sum}