Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram depicts the circle $x^2 + y^2 = 2$ and the line $y = 2x - 1$ meeting at the points $A$ and $B$. The point $D$ on the $x$-axis is positioned so that $AD$ is perpendicular to the $x$-axis.
(a)[4]

Find the exact coordinates of A.

(b)[4]

Find the volume of revolution after the shaded region is turned through $360^\circ$ about the $x$-axis. Give your answer in the form $\frac{\pi}{a}(b\sqrt{c}-d)$, where $a$, $b$, $c$ and $d$ are integers.

(c)[2]

Find a precise expression for the perimeter of the shaded region.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Rewrites as quadratic $5x^2-4x-1=0$” …

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