TMUA Practice Question — Worked Solution

P1·Integration·6.0Mock 0 · P1 · Q14

trapezium ruleoverestimateunderestimatesecond derivativeconcavityindicesparameter

The trapezium rule, with the same number of strips each time, is used to estimate the two integrals

\int_{1}^{4} x^{k} d x and \int_{1}^{4} x^{k} x d x

where

k

is a rational constant. The estimate of the first integral is an overestimate and the estimate of the second integral is an underestimate.What are all the possible values of

k

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