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Question-24411




Question Number 24411 by A1B1C1D1 last updated on 17/Nov/17
Answered by mrW1 last updated on 17/Nov/17
∫_(π/2) ^( 0) ∫_2 ^( 0) r^4 cos (2θ) dr dθ  =∫_(π/2) ^( 0) ((−2^5 )/5)cos (2θ)dθ  =−((16)/5)(sin 0−sin π)  =0
$$\int_{\frac{\pi}{\mathrm{2}}} ^{\:\mathrm{0}} \int_{\mathrm{2}} ^{\:\mathrm{0}} {r}^{\mathrm{4}} \mathrm{cos}\:\left(\mathrm{2}\theta\right)\:{dr}\:{d}\theta \\ $$$$=\int_{\frac{\pi}{\mathrm{2}}} ^{\:\mathrm{0}} \frac{−\mathrm{2}^{\mathrm{5}} }{\mathrm{5}}\mathrm{cos}\:\left(\mathrm{2}\theta\right){d}\theta \\ $$$$=−\frac{\mathrm{16}}{\mathrm{5}}\left(\mathrm{sin}\:\mathrm{0}−\mathrm{sin}\:\pi\right) \\ $$$$=\mathrm{0} \\ $$

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