MathDB

Today's calculation of Integral 578

Source: 2010 Osaka Prefecture University entrance exam/Aerospace Enginnering

March 11, 2010

calculusintegrationinequalitieslogarithmsfunctionalgebradomain

Problem Statement

Find the range of

k

for which the following inequality holds for

0\leq x\leq 1

. \int_0^x \frac {dt}{\sqrt {(3 \plus{} t^2)^3}}\geq k\int _0^x \frac {dt}{\sqrt {3 \plus{} t^2}} If necessary, you may use \ln 3 \equal{} 1.10.