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Official 2019 Paper 1 · Q8

Paper 1CalculusFunctions & graphs

The function ff is such that 0<f(x)<10<f(x)<1 for 0≤x≤10\leq x\leq1.

The trapezium rule with nn equal intervals is used to estimate ∫01f(x) dx\displaystyle\int_0^1 f(x)\,\dd x and produces an underestimate.

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

A∫01(f(x)+1) dx\displaystyle\int_0^1(f(x)+1)\,\dd x
B∫012f(x) dx\displaystyle\int_0^1 2f(x)\,\dd x
C∫−10f(x+1) dx\displaystyle\int_{-1}^0 f(x+1)\,\dd x
D∫−10f(−x) dx\displaystyle\int_{-1}^0 f(-x)\,\dd x
E∫01(1−f(x)) dx\displaystyle\int_0^1(1-f(x))\,\dd x

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