[Q2] Perform the numerical integration for the following unction dx 1+x2 Using mid-point method with h=0.2 determine bounds for the approximation error.
[Q2] Perform the numerical integration for the following unction dx 1+x2 Using mid-point method with h=0.2 determine bounds for the approximation error.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![[Q2] Perform the numerical integration for the following unction
dx
1+x2
Using mid-point method with h=0.2 determine bounds for the approximation error.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69d874e0-3168-4ea6-8932-126850152fff%2F2fd85463-fa7a-4cbc-b314-9495c3ba3eb1%2Fehv71na.jpeg&w=3840&q=75)
Transcribed Image Text:[Q2] Perform the numerical integration for the following unction
dx
1+x2
Using mid-point method with h=0.2 determine bounds for the approximation error.
Expert Solution
Step 1
Given that,
Interval is [0,1] and h = 0.2.
Hence the length of each subinterval is 0.2
Form subinterval as [0,0.2], [0.2,0.4], [0.4,0.6], [0.6,0.8] and [0.8,1].
The number of intervals are 5, so n = 5.
Step 2
Now we need to find midpoint f each interval:
Midpoint of [a,b] is,
the midpoint of each interval as follows:
For [0,0.2],
For [0.2,0.4]
For [0.4,0.6]
For [0.6,0.8]
For [0.8,1]
Step 3
Now find the value of a function at each midpoint,
By using midpoint rule,
Let xi be the midpoint of the interval [a,b] then the approximation is called midpoint rule approximation:
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