Standard +0.3 This is a straightforward application of the polar area formula A = ½∫r²dθ with r = 2sin(3θ). It requires knowing the standard formula, squaring to get 4sin²(3θ), using the double angle identity to integrate, and evaluating between given limits. While it's a Further Maths topic, the execution is mechanical with no problem-solving insight needed, making it slightly easier than average overall.
1 The equation of a curve, in polar coordinates, is
$$r = 2 \sin 3 \theta , \quad \text { for } 0 \leqslant \theta \leqslant \frac { 1 } { 3 } \pi .$$
Find the exact area of the region enclosed by the curve between \(\theta = 0\) and \(\theta = \frac { 1 } { 3 } \pi\).
1 The equation of a curve, in polar coordinates, is
$$r = 2 \sin 3 \theta , \quad \text { for } 0 \leqslant \theta \leqslant \frac { 1 } { 3 } \pi .$$
Find the exact area of the region enclosed by the curve between $\theta = 0$ and $\theta = \frac { 1 } { 3 } \pi$.
\hfill \mbox{\textit{OCR FP2 2007 Q1 [4]}}