Previous in Oscillation and Waves Next in Oscillation and Waves
Question Number 34382 by rashedul last updated on 05/May/18
$$\mathrm{how}\:\mathrm{do}\:\mathrm{i}\:\mathrm{prove} \\ $$$$\int_{\mathrm{o}} ^{\mathrm{t}} \mathrm{cos}\:\mathrm{2}\left(\omega\mathrm{t}+\alpha\right)\mathrm{dt}=\mathrm{0} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 05/May/18
$$=\frac{\mid{sin}\left(\mathrm{2}{wt}+\mathrm{2}\alpha\right)\underset{\mathrm{0}} {\overset{{T}} {\mid}}}{\mathrm{2}{w}} \\ $$$$=\frac{{sin}\left(\mathrm{2}{wT}+\mathrm{2}\alpha\right)−{sin}\left(\mathrm{2}\alpha\right)}{\mathrm{2}{w}} \\ $$$${w}=\frac{\mathrm{2}\Pi}{{T}}\:{so}\:\: \\ $$$$=\frac{{sin}\left(\mathrm{4}\Pi+\mathrm{2}\alpha\right)−{sin}\mathrm{2}\alpha}{\mathrm{2}\omega} \\ $$$$=\frac{{sin}\mathrm{2}\alpha−{sin}\mathrm{2}\alpha}{\mathrm{2}{w}} \\ $$$$=\mathrm{0} \\ $$$${i}\:{think}\:{upper}\:{limig}\:{of}\:{intregal}\:{is}\:{T}\:{where}\:{T} \\ $$$${T}=\mathrm{2}\Pi/{w} \\ $$