Question Number 24411 by A1B1C1D1 last updated on 17/Nov/17
Answered by mrW1 last updated on 17/Nov/17
$$\int_{\frac{\pi}{\mathrm{2}}} ^{\:\mathrm{0}} \int_{\mathrm{2}} ^{\:\mathrm{0}} {r}^{\mathrm{4}} \mathrm{cos}\:\left(\mathrm{2}\theta\right)\:{dr}\:{d}\theta \\ $$$$=\int_{\frac{\pi}{\mathrm{2}}} ^{\:\mathrm{0}} \frac{−\mathrm{2}^{\mathrm{5}} }{\mathrm{5}}\mathrm{cos}\:\left(\mathrm{2}\theta\right){d}\theta \\ $$$$=−\frac{\mathrm{16}}{\mathrm{5}}\left(\mathrm{sin}\:\mathrm{0}−\mathrm{sin}\:\pi\right) \\ $$$$=\mathrm{0} \\ $$