TMUA 2017 Paper 1 Q15 — Worked Solution

P1·Integration, Functions, Transformations & Graphs·6.5Official · 2017 · Q15

trapezium-ruleconcavityover-vs-underestimatemulti-statement

It is given that

f (x) = - 2 x^{2} + 10

. Consider the following three curves:

(1)

y = f (x)

(2)

y = f (x + 1)

(3)

the curve

y = f (x + 1)

reflected in the line

y = 6

The trapezium rule is used to estimate the area under each of these three curves between

x = 0

and

x = 1

. State whether the trapezium rule gives an overestimate or underestimate for each of these areas.

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