Question and Answers Forum

All Questions      Topic List

Differential Equation Questions

Previous in All Question      Next in All Question      

Previous in Differential Equation      Next in Differential Equation      

Question Number 131315 by Engr_Jidda last updated on 03/Feb/21

$$Giventhat{y}_n\left(t\right)={\varrho }^t{B}_{n}sin\frac{n\pi }{4}t$$$$Evaluate{\int }_0^4{\left[y_n\left(t\right)\right]}^{2}dt$$

Answered by Ar Brandon last updated on 03/Feb/21

$$\mathcal{I}={\int }_0^4{\varrho }^{2\mathrm{t}}{B}_{\mathrm{n}}{\sin }^2\frac{\mathrm{n}\pi }{4}\mathrm{t}=\frac{4B_{\mathrm{n}}}{\mathrm{n}\pi }{\int }_0^{\mathrm{n}\pi }{\mathrm{e}}^{\frac{8\mathrm{u}}{\mathrm{n}\pi }}{\sin }^2\mathrm{udu}$$$$=\frac{2B_{\mathrm{n}}}{\mathrm{n}\pi }{\int }_0^{\mathrm{n}\pi }{\mathrm{e}}^{\frac{8\mathrm{u}}{\mathrm{n}\pi }}(1-\cos 2\mathrm{u})\mathrm{du}$$

Commented by Ar Brandon last updated on 03/Feb/21

$$\mathrm{Applying}\mathrm{integration}\mathrm{by}-\mathrm{parts}$$$${\mathrm{we}}^{\prime }\mathrm{ll}\mathrm{get}\mathrm{result}.$$

Commented by Engr_Jidda last updated on 03/Feb/21

$$thankyousir$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com