Oxford University MAT 2019 Solved Papers

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Question : 4 of 10

Marks: +1, -0

D. The area between the parabolas with equations

y=x^2+2 a x+a

and

y=a-x^2

equals 9 . The possible values of

a

are

$a=1$ ,
$a=-3$ or $a=3$ ,
$a=-3$ ,
$a=-1$ or $a=1$ ,
$a=1$ or $a=3$ .

Solution:

|∫↙{-a}^0|(x^2+2 a x+a)-(a-x^2)| {d} x|=|[|\;{2 x^3}/{3}+a x^2|]_{-a}^0|=|\;{a^3}/{3}|

so the integral is 9 for

a=3

or

a=-3

.

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