TMUA Official 2017 Paper 2 · Question 11

The function $f(x)$ is increasing and $f(0)=0$ .

The positive constants $a$ and $b$ are such that $a<b$ .

The area of the region enclosed by the curve $y=f(x)$ , the $x$ -axis and the lines $x=a$ and $x=b$ is denoted by $R$ .

The function $g(x)$ is defined by $g(x)=f(x)+2f(b)$ .

Which of the following is an expression for the area enclosed by the curve $y=g(x)$ , the $x$ -axis and the lines $x=a$ and $x=b$ ?

R+(b-a)f(b)

R+2(b-a)f(b)

R+2f(b)-f(a)

R+2f(b)

R+(f(b))^2

R+(f(b))^2-(f(a))^2

R+2(f(b)-f(a))f(b)

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