Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram illustrates the curve $y = \sqrt{x^4 + 4x + 4}$.
(i)[4]

Find the tangent equation to the curve at the point $(0, 2)$.

(ii)[4]

Show that the $x$-coordinates of the intersection points of the line $y = x + 2$ with the curve satisfy $(x + 2)^2 = x^4 + 4x + 4$. Hence determine these $x$-coordinates.

(iii)[4]

The shaded area in the diagram is turned through $360^\circ$ around the $x$-axis. Find the volume of revolution.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Differentiate by applying the chain rule

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