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Daniel J Smith Custom TMUA Set A Paper 2 · Q18

Paper 2Logic & proofCalculusFunctions & graphs

Let ff be a function defined for all real xx, and assume the integral exists

Which one of the following is a sufficient condition for

∫−24f(x) dx=0\int_{-2}^4f(x)\,dx=0
Af(1)=0f(1)=0
Bf(−2)=f(4)=0f(-2)=f(4)=0
Cf(−x)=−f(x)f(-x)=-f(x) for all real xx
Df(x+1)=−f(1−x)f(x+1)=-f(1-x) for all real xx
Ef(x+2)=−f(2−x)f(x+2)=-f(2-x) for all real xx
Ff(x−1)=−f(1−x)f(x-1)=-f(1-x) for all real xx

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