tmua 2019 Q8

tmua · Uk · paper1 1 marks Numerical integration Quadrature Error Bound Derivation

The function f is such that $0 < f(x) < 1$ for $0 \leq x \leq 1$. The trapezium rule with $n$ equal intervals is used to estimate $\int_0^1 f(x) \, dx$ and produces an underestimate.
Using the same number of equal intervals, for which one of the following does the trapezium rule produce an overestimate?

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The function f is such that $0 < f(x) < 1$ for $0 \leq x \leq 1$.
The trapezium rule with $n$ equal intervals is used to estimate $\int_0^1 f(x) \, dx$ and produces an underestimate.

Using the same number of equal intervals, for which one of the following does the trapezium rule produce an overestimate?

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20