For , define . Which of the following describes the sign of on the interval…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

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

(b)

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

(c)

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

(d)

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