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Official 2020 Paper 2 · Q13

Paper 2Logic & proofCalculusFunctions & graphs

f(x)f(x) is a function for which

∫03(f(x))2 dx+∫03f(x) dx=∫01f(x) dx\int_0^3(f(x))^2\,\dd x+\int_0^3 f(x)\,\dd x=\int_0^1 f(x)\,\dd x

Which of the following claims about f(x)f(x) is/are necessarily true?

  • I f(x)≤0f(x)\leq0 for some xx with 1≤x≤31\leq x\leq3
  • II ∫03f(x) dx≤∫01f(x) dx\displaystyle\int_0^3 f(x)\,\dd x\leq\int_0^1 f(x)\,\dd x
Aneither of them
BI only
CII only
DI and II

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