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Gresty Academy Paper 2 · Q12

Paper 2Logic & proofCalculus

How many of the following statements are necessary for

∫13f(x) dx=0\int_1^3 f(x)\,\mathrm dx=0

to hold true?

  • f(x)<0f(x)<0 for some x∈[1,3]x\in[1,3]
  • f(x)≤0f(x)\leq0 for some x∈[1,3]x\in[1,3]
  • f(x)>0f(x)>0 for some x∈[1,3]x\in[1,3]
  • f(x)≥0f(x)\geq0 for some x∈[1,3]x\in[1,3]
  • ∫11.5f(x) dx=−∫1.53f(x) dx\displaystyle\int_1^{1.5}f(x)\,\mathrm dx=-\int_{1.5}^3f(x)\,\mathrm dx
A00
B11
C22
D33
E44

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