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Official 2017 Paper 2 · Q10

Paper 2Logic & proofCalculusFunctions & graphs

f(x)f(x) is a function defined for all real values of xx.

Which one of the following is a sufficient condition for ∫13f(x) dx=0\displaystyle\int_1^3 f(x)\,\dd x=0?

Af(2)=0f(2)=0
Bf(1)=f(3)=0f(1)=f(3)=0
Cf(−x)=−f(x)f(-x)=-f(x) for all xx
Df(x+2)=−f(2−x)f(x+2)=-f(2-x) for all xx
Ef(x−2)=−f(2−x)f(x-2)=-f(2-x) for all xx

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