Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 81889 by rajesh4661kumar@gmail.com last updated on 16/Feb/20

Answered by john santu last updated on 16/Feb/20

$$let\sqrt{x}=\sin t\Rightarrow x=\sin {}^{2}t$$$$dx=2\sin t\cos tdt$$$$\Rightarrow I=\int \sqrt{\frac{1-\sin t}{1+\sin t}}\left(2\sin t\cos t\right)dt$$$$=\int \frac{(1-\sin t)2\sin t\cos t}{\cos t}dt$$$$=\int (1-\sin t)2\sin tdt$$$$=\int 2\sin t-2(\frac{1}{2}-\frac{1}{2}\cos 2t)dt$$$$=-2\cos t-t+\frac{1}{2}\sin 2t+c$$$$=-2\sqrt{1-x}-{\sin }^{-1}\left(\sqrt{x}\right)+\sqrt{x-x^2}+c$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com