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MioMath 2024 Paper 2 · Q13

Paper 2Logic & proofCalculus

Given that f′(x)<0f'(x)<0 for 0≤x≤10\le x\le1, which of the following statements must be true?

  • I. ∫01/2f(x)dx>∫1/21f(x)dx\displaystyle\int_0^{1/2}f(x)\dd x>\int_{1/2}^1f(x)\dd x
  • II. ∫01/2f(x)dx<∫01/2f(x2)dx\displaystyle\int_0^{1/2}f(x)\dd x<\int_0^{1/2}f(x^2)\dd x
  • III. f(0)<f(1)f(0)<f(1)
AOnly I
BOnly II
COnly III
DI and II
EI and III
FII and III
GAll of them

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