TMUA 2021 Paper 1 Q7 — Worked Solution

P1·Integration, Functions, Transformations & Graphs·6.5Official · 2021 · Q7

definite-integralmodulus-integrandgraph-transformation

The function

f

is such that

f (0) = 0

, and

x f (x) > 0

for all non-zero values of

x

. It is given that

\int_{- 2}^{2} f (x) d x = 4 and \int_{- 2}^{2} ∣ f (x) ∣ d x = 8.

Evaluate

\int_{- 2}^{0} f (∣ x ∣) d x .

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