Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram presents a section of the curve $y = \frac{2}{(3 - 2x)^2} - x$ together with its minimum point $M$, which is situated on the $x$-axis.

(a)[6]

Determine expressions for $\frac{dy}{dx}$, $\frac{d^2y}{dx^2}$ and $\int y\,dx$.

(b)[2]

Calculate the $x$-coordinate of $M$.

(c)[2]

Calculate the area of the shaded region enclosed by the curve and the coordinate axes.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Gives $\frac{dy}{dx}=\frac{8}{(3-2x)^3}$” …