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
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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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.
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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