tmua.me Medium Set C Paper 2 · Question 9

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tmua.me Medium Set C Paper 2 · Q9

Paper 2GeometryAlgebra

For $1\leq x\leq2$ , the curve $C$ has equation

y=\frac{x^3+1}{x^2}.

A horizontal line $y=k$ has the following property: within the strip $1\leq x\leq2$ , the total area between $C$ and the line where $C$ is above the line equals the total area between them where $C$ is below the line.

What is $k$ ?

\dfrac32

\dfrac74

2

\dfrac{17}{8}

\dfrac94

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