WRITE A C++ PROGRAM TO IMPLEMENT THE MID POINT RULE NUMERICAL APPROXIMATION Midpoint RuleIf we consider the case where x is chosen to be the midpoint ; of the subinterval [x;-1, x;]. Then wehaveь — а| f(x) dx = M,n = Ax[f(F1)+ f (T2) + + · · · + f(Tm)], where Axand õi(Xi-1+ xi)•.nAs shown in the figure belowy A(c) Midpoint approximationThe following algorithm uses the Midpoint Rule on n subintervals to approximate Idx:• INPUT endpoints a, b; positive integer n.• OUTPUT approximate solution XI to I.- a• Step 1 Set h• Step 2 Set XI = 0; Xbar= a + 5:- Step 3 For i = 1,2,-- Step 4 Set XI = XI+ f(Xbar)Step 5 Set i = i +1...n do Steps 4 to 6.Step 6 Set Xbar = Xbar +h-• Step 7 XI = XI * h.• Step 8 OUTPUT(XI) and STOP.

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Engineering

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WRITE A C++ PROGRAM TO IMPLEMENT THE MID POINT RULE NUMERICAL APPROXIMATION

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter13: Structures

Section: Chapter Questions

Problem 4PP

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Question

WRITE A C++ PROGRAM TO IMPLEMENT THE MID POINT RULE NUMERICAL APPROXIMATION

Midpoint Rule
If we consider the case where x is chosen to be the midpoint ; of the subinterval [x;-1, x;]. Then we
have
ь — а
| f(x) dx = M,n = Ax[f(F1)+ f (T2) + + · · · + f(Tm)], where Ax
and õi
(Xi-1+ xi)
•.
n
As shown in the figure below
y A
(c) Midpoint approximation
The following algorithm uses the Midpoint Rule on n subintervals to approximate I
dx:
• INPUT endpoints a, b; positive integer n.
• OUTPUT approximate solution XI to I.
- a
• Step 1 Set h
• Step 2 Set XI = 0; Xbar
= a + 5:
- Step 3 For i = 1,2,-
- Step 4 Set XI = XI+ f(Xbar)
Step 5 Set i = i +1
...n do Steps 4 to 6.
Step 6 Set Xbar = Xbar +h
-
• Step 7 XI = XI * h.
• Step 8 OUTPUT(XI) and STOP.

Process by which instructions are given to a computer, software program, or application using code.

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