TMUA 2019 Paper 2 Q13 — Worked Solution

P2·Integration, Trigonometry·6.5Official · 2019 · Q13

trapezium-rulesymmetrytrig-identity

A student approximates the integral

\int_{a}^{b} sin^{2} x d x

using the trapezium rule with 4 strips. The resulting approximation is an overestimate.

If the student approximates

\int_{- b}^{- a} sin^{2} x d x

in the same way, the result will be an overestimate.

If the student approximates

\int_{a}^{b} cos^{2} x d x

in the same way, the result will be an underestimate.

Which of these statements is/are necessarily true?

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