TMUA 2023 Paper 2 Q20 — Worked Solution

P2·Integration·7.0Official · 2023 · Q20

even-odd-symmetrydefinite-integralmust-be-true

Let

f

be a polynomial with real coefficients.The integral

I_{p, q}

where

p < q

is defined by

I_{p, q} = \int_{p}^{q} ((f (x))^{2} - (f (∣ x ∣))^{2}) d x .

Which of the following statements must be true?

I_{p, q} = 0

only if

0 < p

f^{'} (x) < 0

for all

x

only if

I_{p, q} < 0

for all

p < q < 0

I_{p, q} > 0

only if

p < 0

All questions

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