TMUA 2020 Paper 2 Q6 — Worked Solution

P2·Integration, Logic & Quantifiers·6.0Official · 2020 · Q6

necessary-conditiondefinite-integralsymmetry

The function

f (x)

is defined for all real values of

x

. Consider the equation

\int_{- 5}^{0} f (x) d x = \int_{0}^{5} f (x) d x .

Which of the following conditions on

f (x)

is/are necessary to ensure that the equation holds?

f (x) = f (- x)

for

- 5 \leq x \leq 5

f (x) = c

for

- 5 \leq x \leq 5

, where

c

is a constant

III

f (x) = - f (- x)

for

- 5 \leq x \leq 5

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