TMUA Practice Question — Worked Solution

P1·Integration·6.0Mock 0 · P1 · Q9

odd functioncombining rangesarea vs integraltranslationsymmetry

The function

f

satisfies

f (- x) = - f (x)

for all real

x

. Also,

f (x) > 0

for

0 < x < 1

, and

f (x) < 0

for

x > 1

.The total area of the regions enclosed by the curve

y = f (x)

, the

x

-axis and the lines

x = - 1

and

x = 3

16

, and

\int_{0}^{3} f (x) d x = - 4.

What is the value of

\int_{- 2}^{2} f (x + 1) d x ?

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