Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram displays part of the curve $y = 8 - \sqrt{(4 - x)}$ together with the tangent to the curve at $P\,(3, 7)$.

(i)[5]

Find expressions for $\frac{dy}{dx}$ and $\int y\,dx$.

(ii)[2]

Find the equation of the tangent to the curve at $P$ in the form $y = mx + c$.

(iii)[4]

Find, showing all necessary working, the area of the shaded region.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiates $y=8-\sqrt{4-x}$ correctly” …