I = 피(1-22)dz:
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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Question
Transcribed Image Text:Q4)
In §2.5 we introduced the trapezoid rule for computing integrals. Recall that, for equally
spaced points, the approximation takes the form
T„(f) = ; (S(20) + 2f(71) + … · + 2f(xn=1) + f(an))
Improvement of the approximation: Define the new quadrature rule,
which we will call the corrected trapezoid rule. This value will tend to be
much more accurate than that obtained using the ordinary trapezoid rule and
only marginally more expensive to compute.
Apply the trapezoid rule and corrected trapezoid rule, with h = }, to approximate
the integral
1
I =
2(1 – 2²)dz = -
=
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In this question, we use the given formula to evaluate the integral of
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