3. (a) The trapezium rule for integrating a function over the interval [-h, h] can be written in the form | f(z) dz = wof(-h) + wif(h) + Ks"(€), (3.1) where wo and wi are constant weights and the final term on the right-hand side is the error term with E (-h, h). Describe briefly the method of undetermined coefficients, then use it to find the constants wo, w and K.

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3. (a) The trapezium rule for integrating a function over the interval [-h, h] can be written in
the form
f(r) dr = wof(-h) + wif(h) + Kf"(E),
(3.1)
%3D
where wo and wi are constant weights and the final term on the right-hand side is the
error term with E (-h, h). Describe briefly the method of undetermined coefficients,
then use it to find the constants wo, wi and K.
Transcribed Image Text:3. (a) The trapezium rule for integrating a function over the interval [-h, h] can be written in the form f(r) dr = wof(-h) + wif(h) + Kf"(E), (3.1) %3D where wo and wi are constant weights and the final term on the right-hand side is the error term with E (-h, h). Describe briefly the method of undetermined coefficients, then use it to find the constants wo, wi and K.
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