(i)[1]
Determine the value of $k$.
(ii)[2]
Show that the curve meets the line $y = x$ again when $x = 5$.
(iii)[5]
Find the area of the shaded region, showing all necessary working.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The diagram depicts a section of the curve with equation $y = k(x^3 - 7x^2 + 12x)$, where $k$ is a constant. The curve cuts the line $y = x$ at the origin $O$ and again at the point $A(2, 2)$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use equation $2=k(8-28+24)$ and solve to get $k=\frac{1}{2}$” …
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