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 142443 by Hassen_Timol last updated on 31/May/21

F(x) = ∫_( x) ^( x^2 ) (1/( ln(t) )) dt Show that : ∣ F(x) ∣ ≤ ((∣ x^2 − x ∣)/(∣ ln(x) ∣)) Please

F(x)=∫xx21ln(t)dtShowthat:∣F(x)∣⩽∣x2−x∣∣ln(x)∣Please

Answered by Boucatchou last updated on 31/May/21

∀ x≤t≤x^2 ,x>0, (1/(lnt))≤(1/(lnx)) ⇒ ∣F(x)∣≤∫_x ^( x^2 ) (1/(∣lnt∣))dt≤(1/(∣lnx∣))∫_x ^( x^2 ) dt ⇒ ∣F(x)≤((x^2 −x^x )/(∣lnx∣))≤((∣x^2 −x∣)/(∣lnx∣))

∀x⩽t⩽x2,x>0,1lnt⩽1lnx⇒∣F(x)∣⩽∫xx21∣lnt∣dt⩽1∣lnx∣∫xx2dt⇒∣F(x)⩽x2−xx∣lnx∣⩽∣x2−x∣∣lnx∣

Terms of Service

Privacy Policy

Contact: info@tinkutara.com