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 21707 by Isse last updated on 01/Oct/17

$${\int }_{\pi /6}^{\pi /3}\frac{1}{2}{cot}^{2}2\theta d\theta$$

Commented by Tikufly last updated on 01/Oct/17

$$\mathrm{I}=\frac{1}{2}{\int }_{\pi /6}^{\pi /3}({\mathrm{cosec}}^{2}2\theta -1)\mathrm{d}\theta$$$$=\frac{1}{2}{\int }_{\pi /6}^{\pi /3}{\mathrm{cosec}}^{2}2\theta -\frac{1}{2}{\int }_{\pi /6}^{\pi /3}1\mathrm{d}\theta$$$$=-\frac{1}{4}{\left[\cot 2\theta \right]}_{\pi /6}^{\pi /3}-\frac{1}{2}{\left[\theta \right]}_{\pi /6}^{\pi /3}$$$$=-\frac{1}{4}\{\cot \left(\frac{2\theta }{3}\right)-\cot \left(\frac{\theta }{3}\right)\}-\frac{1}{2}(\frac{\pi }{3}-\frac{\pi }{6})$$$$=-\frac{1}{4}(-\frac{1}{\sqrt{3}}-\frac{1}{\sqrt{3}})-\frac{1}{2}\left(\frac{\pi }{6}\right)$$$$=\frac{1}{2\sqrt{3}}-\frac{\pi }{12}$$

Commented by Isse last updated on 01/Oct/17

$$thanks$$

Commented by Tikufly last updated on 02/Oct/17

$$\mathrm{Welcome}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com