17M.2.AHL.TZ2.H_2

pestleMathematicsAAHLPaper 217M· ahl-5-17-areas-under-curve-onto-y-axis-volume-of-revolution-(about-x-and-y-axes)source ↗

Consider the curve defined by the equation $4{x^2} + {y^2} = 7$ .

Find the volume of the solid formed when the region bounded by the curve, the $x$ -axis for $x \geqslant 0$ and the $y$ -axis for $y \geqslant 0$ is rotated through $2\pi$ about the $x$ -axis.

Markscheme / solution

Use of $V = \pi \int\limits_0^{\frac{{\sqrt 7 }}{2}} {{y^2}{\text{d}}x}$

$V = \pi \int\limits_0^{\frac{{\sqrt 7 }}{2}} {\left( {7 - 4{x^2}} \right){\text{d}}x}$ (M1)(A1)

Note: Condone absence of limits or incorrect limits for M mark.

Do not condone absence of or multiples of $\pi$ .

$= 19.4\,\,\,\left( { = \frac{{7\sqrt 7 \pi }}{3}} \right)$ A1

[3 marks]

Examiners’ report

[N/A]