Find the equation of the vertical asymptote to the graph of $f$.

Find the $x$-intercept of the graph of $f$.

The region enclosed by the graph of $f$, the $x$-axis and the line $x = 10$ is rotated $360$° about the $x$-axis. Find the volume of the solid formed.

valid approach     (M1)

eg$\;\;\;$horizontal translation $3$ units to the right

$x = 3$ (must be an equation)     A1     N2

[2 marks]

valid approach     (M1)

eg$\;\;\;f(x) = 0,{\text{ }}{e^0} = x - 3$

$4,{\text{ }}x = 4,{\text{ }}(4,{\text{ }}0)$     A1     N2

[2 marks]

attempt to substitute either their correct limits or the function into formula involving ${f^2}$      (M1)

eg$\;\;\;\int_4^{10} {{f^2},{\text{ }}\pi \int {{{\left( {2\ln (x - 3)} \right)}^2}{\text{d}}x} }$

$141.537$

volume = $142$     A2     N3

[3 marks]

Total [7 marks]