Mathematics

Problem

For

x>0

, define

R(x)=\displaystyle \int_{x}^{x^{2}} \ln\bigl(1+t^{2}\bigr)\,dt

. Which of the following describes the sign of

R'(x)

on the interval

0<x<1

? a)

R'(x)=0\text{ for all }0<x<1

R'(x)>0\text{ for all }0<x<1

R'(x)\text{ changes sign on }(0,1)

R'(x)<0\text{ for all }0<x<1