<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Show that \(\cos 3\theta = 4\cos^3 \theta - 3\cos \theta\).</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence, or otherwise, evaluate \(\displaystyle\int\nolimits_0^{\frac{\pi}{6}} \sin 2\theta \cos 3\theta \, \mathrm{d}\theta\) exactly.</span><span class="inline-marks">[4]</span></div></li></ol>

Show that \(\cos 3\theta = 4\cos^3 \theta - 3\cos \theta\).

Hence, or otherwise, evaluate \(\displaystyle \displaystyle\int\nolimits_0^{\frac{\pi}{6}} \sin 2\theta \cos 3\theta \, \mathrm{d}\theta\) exactly.

Techniques of  Integration

International Baccalaureate Higher Level Mathematics

2025 ASRJC P1 Q2

2025 ASRJC P1 Q2