Shortcut for the Trapezoid Rule Prove that if you have

Chapter 5, Problem 58AE

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QUESTION:

Shortcut for the Trapezoid Rule  Prove that if you have M(n) and T(n) (a Midpoint Rule approximation and a Trapezoid Rule approximation with n subintervals), then T(2n)=(T(n)+M(n))/2.

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QUESTION:

Shortcut for the Trapezoid Rule  Prove that if you have M(n) and T(n) (a Midpoint Rule approximation and a Trapezoid Rule approximation with n subintervals), then T(2n)=(T(n)+M(n))/2.

ANSWER:

Solution:-

Step1

Given that

A Midpoint Rule approximation and a Trapezoid Rule approximation with n subintervals.

Step2

Prove that

Step3

 The Midpoint Rule is the approximation of

+-------+]

The Trapezoidal  Rule is the approximation of

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