Problem 22. Using the Trapezoidal Rule for xp: a. Estimate the integral with n = 4 steps and find an upper bound M(b – a)3 12n2 for |En(f,T)|. b. Evaluate the integral directly and find |En(f,T)| precisely. c. Use the formula |En(f,T)| x 100% the true value to express |E„(f,T)| as a percentage of the integral's true value.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Problem 22

Problem 22. Using the Trapezoidal Rule for
1
dax,
a. Estimate the integral with n = 4 steps and find an upper bound
M(b – a)3
12n2
for |En(f,T)|.
b. Evaluate the integral directly and find |En(f,T)| precisely.
c. Use the formula
|En(f,T)|
the true valие
x 100%
to express |En(f,T)| as a percentage of the integral's true value.
Solution:
Transcribed Image Text:Problem 22. Using the Trapezoidal Rule for 1 dax, a. Estimate the integral with n = 4 steps and find an upper bound M(b – a)3 12n2 for |En(f,T)|. b. Evaluate the integral directly and find |En(f,T)| precisely. c. Use the formula |En(f,T)| the true valие x 100% to express |En(f,T)| as a percentage of the integral's true value. Solution:
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