Challenging +1.2 This is a standard Further Maths polar area question requiring the formula A = ½∫r²dθ. While it involves a moderately complex integrand (requiring substitution u = sin θ and binomial expansion), the method is routine for FP3 students and the question explicitly tells them what answer to show, removing uncertainty about correctness during working.
6 The diagram shows a sketch of a curve \(C\).
\includegraphics[max width=\textwidth, alt={}, center]{8cb4b110-274e-47ec-a31b-ee8f84434a65-3_305_556_1078_721}
The polar equation of the curve is
$$r = 2 \sin 2 \theta \sqrt { \cos \theta } , \quad 0 \leqslant \theta \leqslant \frac { \pi } { 2 }$$
Show that the area of the region bounded by \(C\) is \(\frac { 16 } { 15 }\).
6 The diagram shows a sketch of a curve $C$.\\
\includegraphics[max width=\textwidth, alt={}, center]{8cb4b110-274e-47ec-a31b-ee8f84434a65-3_305_556_1078_721}
The polar equation of the curve is
$$r = 2 \sin 2 \theta \sqrt { \cos \theta } , \quad 0 \leqslant \theta \leqslant \frac { \pi } { 2 }$$
Show that the area of the region bounded by $C$ is $\frac { 16 } { 15 }$.
\hfill \mbox{\textit{AQA FP3 2011 Q6 [7]}}