The diagram depicts a section of the curve with equation $y = \frac{4}{(2x - 1)^2}$ together with sections of the lines $x = 1$ and $y = 1$. The curve goes through the points $A(1, 4)$ and $B\left(\frac{3}{2}, 1\right)$.
(a)[5]
Find the exact volume produced when the shaded region is turned through $360^\circ$ about the $x$-axis.
(b)[6]
A triangle is bounded by the tangent to the curve at $B$, the normal to the curve at $B$ and the $x$-axis. Find the area of this triangle.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate integration of $\frac{16}{(2x-1)^4}$” …