TMUA Official 2020 Paper 2 · Question 6 · ExamDay

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Official 2020 Paper 2 · Q6

Paper 2Logic & proofCalculusFunctions & graphs

The function $f(x)$ is defined for all real values of $x$ .

Which of the following conditions on $f(x)$ is/are necessary to ensure that

\int_{-5}^0 f(x)\,\dd x=\int_0^5 f(x)\,\dd x

Condition I: $f(x)=f(-x)$ for $-5\leq x\leq5$
Condition II: $f(x)=c$ for $-5\leq x\leq5$ , where $c$ is a constant
Condition III: $f(x)=-f(-x)$ for $-5\leq x\leq5$

Anone of them

BI only

CII only

DIII only

EI and II only

FI and III only

GII and III only

HI, II and III

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