(i)[5]
Find, showing all necessary working, the volume produced when the shaded region is turned through $360^\circ$ about the $x$-axis.
(ii)[5]
Find the equation of the normal to the curve at $A$, and give your answer in the form $y = mx + c$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The diagram gives part of the curve $y = 2(3x - 1)^{-\frac{1}{3}}$ together with the lines $x = \frac{2}{3}$ and $x = 3$. The curve meets the line $x = \frac{2}{3}$ at the point $A$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct volume integral set up, $V=4\pi\int(3x-1)^{-2/3}dx$.” …
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