(a)[5]
Show that the line $PQ$ is a normal to the curve.
(b)[7]
Find the exact volume of revolution, showing all necessary working, when the shaded region is rotated through $360^\circ$ about the $x$-axis.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The diagram shows a section of the curve $y = \sqrt{1 + 4x}$, together with the point $P(6,5)$ on the curve. The line $PQ$ cuts the $x$-axis at $Q(8,0)$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $y=\sqrt{1+4x}$ to obtain $\frac{dy}{dx}=\frac12(1+4x)^{-\frac{1}{2}}\cdot4$” …
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