3. The numerical error introduced by using the Trapezoidal rule to approximate a definite inte- gral is given by Er = | f(x) dx – T, where T is the estimate of the definite integral (calculated using the Trapezoidal rule). The error can be bound by b — а |Er| < 12 where M is any upper bound for the values of |f"(x)| on [a, b]. (a) Find an upper bound on the error when the trapezoidal rule with n = 10 is used to estimate the value of x sin x dx.
3. The numerical error introduced by using the Trapezoidal rule to approximate a definite inte- gral is given by Er = | f(x) dx – T, where T is the estimate of the definite integral (calculated using the Trapezoidal rule). The error can be bound by b — а |Er| < 12 where M is any upper bound for the values of |f"(x)| on [a, b]. (a) Find an upper bound on the error when the trapezoidal rule with n = 10 is used to estimate the value of x sin x dx.
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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Transcribed Image Text:3. The numerical error introduced by using the Trapezoidal rule to approximate a definite inte-
gral is given by
ET
| f(x) dx – T ,
a
where T is the estimate of the definite integral (calculated using the Trapezoidal rule). The
error can be bound by
a
|Er| < "h?M
12
where M is any upper bound for the values of f"(x)| on [a, b).
(a) Find an upper bound on the error when the trapezoidal rule with n =
10 is used to
estimate the value of
x sin x dx.
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