Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The curve satisfies $\frac{dy}{dx}=6x^2+\frac{k}{x^3}$ and it passes through the point $P(1,9)$. The gradient at $P$ is $2$.

(a(i))[1]

Determine the constant $k$.

(a(ii))[4]

Determine the equation of the curve.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct working showing $6+k=2 \Rightarrow k=-4$” …