TMUA 2020 Paper 2 Q13 — Worked Solution

P2·Integration, Logic & Quantifiers·6.5Official · 2020 · Q13

definite-integralmust-be-trueintegral-inequalities

f (x)

is a function for which

\int_{0}^{3} (f (x))^{2} d x + \int_{0}^{3} f (x) d x = \int_{0}^{1} f (x) d x .

Which of the following claims about

f (x)

is/are necessarily true?

f (x) \leq 0

for some

x

with

1 \leq x \leq 3

\int_{0}^{3} f (x) d x \leq \int_{0}^{1} f (x) d x

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