tmua.me Medium Set D Paper 1 · Question 14

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tmua.me Medium Set D Paper 1 · Q14

Paper 1CalculusGeometryFunctions & graphs

A continuous function $f$ satisfies $f(0)=f(1)=f(4)=0$ . Its graph lies above the $x$ -axis for $0<x<1$ and below the $x$ -axis for $1<x<4$ .

The area between the graph and the $x$ -axis is $5$ for $0\leq x\leq1$ and $2$ for $1\leq x\leq4$ .

What is the value of

\int_0^4\bigl(2f(x)-3\bigr)\,dx?

-18

-6

2

3

6

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