Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 111039 by mathdave last updated on 01/Sep/20

$$solve$$$${\int }_0^1\sqrt{1+x^6}dx$$$$mrabboyourquestion$$

Answered by mathdave last updated on 01/Sep/20

$$letI={\int }_0^1\sqrt{1+x^6}dx$$$$letu=x^6$$$$I=\frac{1}{6}{\int }_0^1{u}^{-\frac{5}{6}}{(1+u)}^{\frac{1}{2}}du$$$$byhypergeometricgeneralizationformula$$$$\beta (b,c-b)2f_1(a,b,c:z)={\int }_0^1{x}^{b-1}{(1-x)}^{c-b-1}{(1-zx)}^{-a}$$$$I=\frac{1}{6}{\int }_0^1{u}^{\frac{1}{6}-1}{(1-u)}^{\frac{7}{6}-\frac{1}{6}-1}{(1-(-u))}^{-(-\frac{1}{2})}$$$$I=\frac{\beta \left({\frac{1}{6}}^{\prime }1\right)}{6}2f_1(-\frac{1}{2},\frac{1}{6},\frac{7}{6},:-1)=1.06409$$$$\because {\int }_0^1\sqrt{1+x^6}dx=1.06409$$$$mathdave\left(01/09/2020\right)$$

Commented by abdomsup last updated on 01/Sep/20

$$sorryihsvereditbyeroorthank$$$$youfortheanswer$$

Commented by Rasheed.Sindhi last updated on 02/Sep/20

$$OnlytoremoveredmarkIclicked$$$$likebutton.ActuallyI{haven}^{\prime }t$$$$readthepost.$$

Commented by mathdave last updated on 02/Sep/20

$$idontreallygetwhatyoupeopleare$$$$saying$$

Commented by Rasheed.Sindhi last updated on 02/Sep/20

$$mathdavesir$$$$Iwantedtosayonlythat,$$$$mathmaxsirunintetionally$$$$markedyouranswerredandI$$$$wantedtoremovethatredmark.$$$$soIwithoutreadingyour$$$$answerclickedonlike-button\left(\mathrm{♡}\right)$$$$forremovingredmark.$$$$Inthisappifapersonmarks$$$$redapostandanotherperson$$$${}^{\prime }{likes}^{\prime }thatpostthenredmark$$$$clears.$$

Commented by mathdave last updated on 02/Sep/20

$$nowiunderstandweller,thanksfor$$$$yournotion$$

Commented by Eric002 last updated on 04/Sep/20

$$niceworksir$$

Commented by abdomsup last updated on 08/Sep/20

$$thankyousirrashed$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com