Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 7021 by FilupSmith last updated on 06/Aug/16

$$z={\int }_0^{t}i{(-1)}^{x}dx$$$$={\int }_0^t{ie}^{i\pi x}dx$$$$$$$$\left(1\right)$$$$=i{\int }_0^t{e}^{i\pi x}dx$$$$=i\left(\frac{1}{i\pi }(e^{i\pi t}-1)\right)$$$$z=\frac{1}{\pi }({(-1)}^t-1)$$$$$$$$\left(2\right)$$$$={\int }_0^t{ie}^{i\pi x}dx$$$$u=e^{i\pi x}\Rightarrow du=\frac{1}{i\pi }{e}^{i\pi x}dx$$$$={\int }_0^t\frac{i\pi }{i\pi }{ie}^{i\pi x}dx$$$$={\int }_0^{t}i\pi idu$$$$=-\pi {\int }_0^{t}du$$$$=-\pi (e^{i\pi t}-1)$$$$$$$$\mathrm{which}\mathrm{is}\mathrm{incorrect}?$$

Commented by FilupSmith last updated on 07/Aug/16

$$\mathrm{Ah},\mathrm{i}\mathrm{see}\mathrm{my}\mathrm{mistake},\mathrm{thank}\mathrm{you}!$$

Commented by Yozzii last updated on 06/Aug/16

$$In\left(2\right),foru=e^{i\pi x}\Rightarrow du=i\pi e^{i\pi x}dx$$$$\Rightarrow u=e^{\pi it}atx=tandu=1atx=0.$$$$\Rightarrow {\int }_0^t{ie}^{\pi ix}dx=i\times \frac{1}{i\pi }{\int }_1^{e^{i\pi t}}du=\frac{1}{\pi }(e^{\pi it}-1)=\frac{1}{\pi }({(-1)}^t-1)$$$$$$

Answered by Yozzii last updated on 08/Aug/16

$$Checkforaresponseinthecomments.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com