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 11998 by ajfour last updated on 09/Apr/17

Commented by ajfour last updated on 09/Apr/17

What distance does point P   travel as the centre moves   forward by 2πR . The disc   rolls witbout slipping .

$${What}\:{distance}\:{does}\:{point}\:{P}\: \\ $$$${travel}\:{as}\:{the}\:{centre}\:{moves}\: \\ $$$${forward}\:{by}\:\mathrm{2}\pi{R}\:.\:{The}\:{disc} \\ $$$$\:{rolls}\:{witbout}\:{slipping}\:. \\ $$

Commented by mrW1 last updated on 10/Apr/17

length of trochoid (r≤R)  L=∫_0 ^(2π) (√(R^2 +r^2 −2Rrcos θ)) dθ

$${length}\:{of}\:{trochoid}\:\left({r}\leqslant{R}\right) \\ $$$${L}=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \sqrt{{R}^{\mathrm{2}} +{r}^{\mathrm{2}} −\mathrm{2}{Rr}\mathrm{cos}\:\theta}\:{d}\theta \\ $$

Commented by ajfour last updated on 10/Apr/17

thanks, this is true but couple   of months back you explained  solution to this integral as well.  that dint seem to match with  the case r=R even; for which  the answer is L=8R .Kindly  solve this integral too..

$${thanks},\:{this}\:{is}\:{true}\:{but}\:{couple}\: \\ $$$${of}\:{months}\:{back}\:{you}\:{explained} \\ $$$${solution}\:{to}\:{this}\:{integral}\:{as}\:{well}. \\ $$$${that}\:{dint}\:{seem}\:{to}\:{match}\:{with} \\ $$$${the}\:{case}\:{r}={R}\:{even};\:{for}\:{which} \\ $$$${the}\:{answer}\:{is}\:{L}=\mathrm{8}{R}\:.{Kindly} \\ $$$${solve}\:{this}\:{integral}\:{too}.. \\ $$

Commented by mrW1 last updated on 10/Apr/17

For r≠R the integral is not easy.   In Wolfram you can read more details.

$${For}\:{r}\neq{R}\:{the}\:{integral}\:{is}\:{not}\:{easy}.\: \\ $$$${In}\:{Wolfram}\:{you}\:{can}\:{read}\:{more}\:{details}. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com