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 68481 by ajfour last updated on 11/Sep/19

$$I={\int }_0^1\sqrt{\frac{c-x^2}{x(1-x^2)}}dx(c>1)$$

Commented by MJS last updated on 11/Sep/19

$$\mathrm{I}\mathrm{tried}\mathrm{everything}\mathrm{I}\mathrm{know},\mathrm{it}\mathrm{seems}\mathrm{impossible}$$$$\mathrm{to}\mathrm{solve}$$

Commented by Kunal12588 last updated on 12/Sep/19

Commented by Kunal12588 last updated on 12/Sep/19

Commented by MJS last updated on 12/Sep/19

$$\frac{2x\sqrt{1-x^2}\sqrt{\frac{c-x^2}{x-x^3}}}{\sqrt{1-\frac{x^2}{c}}}=2\sqrt{cx}$$$$\Rightarrow {\left[2\sqrt{cx}{\mathrm{F}}_1(...)\right]}_0^1=2\sqrt{c}{\mathrm{F}}_1(\frac{1}{4};-\frac{1}{2},\frac{1}{2};\frac{5}{4};\frac{1}{c},1)$$

Commented by MJS last updated on 12/Sep/19

$$\mathrm{Sir}\mathrm{Kunal},\mathrm{can}\mathrm{you}\mathrm{calculate}\mathrm{it}\mathrm{now}?$$

Commented by MJS last updated on 12/Sep/19

$$\mathrm{I}\mathrm{found}\mathrm{this}:$$$${\mathrm{F}}_1(a,b_1,b_2,c;x;y)=\frac{\mathrm{\Gamma }\left(c\right)}{\mathrm{\Gamma }\left(a\right)\mathrm{\Gamma }(c-a)}\underset{0}{\stackrel{1}{\int }}{t}^{a-1}{(1-t)}^{c-a-1}{(1-xt)}^{-b_1}{(1-yt)}^{-b_2}dt$$$$\mathrm{in}\mathrm{our}\mathrm{case}\mathrm{this}\mathrm{leads}\mathrm{to}$$$$\frac{\sqrt{c}}{2}\underset{0}{\stackrel{1}{\int }}\frac{\sqrt{c-t}}{t^{3/4}\sqrt{c(1-t)}}dt$$$$...\mathrm{but}\mathrm{is}\mathrm{this}\mathrm{easier}?$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com