TMUA 2021 Paper 1 Q15 — Worked Solution

P1·Integration, Functions, Transformations & Graphs·7.0Official · 2021 · Q15

area-under-graphhorizontal-scalingsum-of-integrals

The diagram shows the graph of

y = f (x)

The graph consists of alternating straight-line segments of gradient

1

and

- 1

and continues in this way for all values of

x

.The function

g

is defined as

g (x) = r = 1 \sum 10 f (2^{r - 1} x) .

Find the value of

\int_{0}^{1} g (x) d x .

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