Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram depicts a segment of the curve $y = \frac{1}{2}(x^4 - 1)$, which is defined for $x \geq 0$.

(i)[3]

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

(ii)[4]

Find, showing all necessary working, the volume generated when the shaded region is turned through $360^\circ$ about the $x$-axis.

(iii)[5]

Find, showing all necessary working, the volume generated when the shaded region is turned through $360^\circ$ about the $y$-axis.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Integrate to obtain the area expression” …