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Application of Derivatives question

2012 · Shift 2 · Q29

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PYQ Library
JEE Advanced
Mathematics
Application of Derivatives
2012 · Shift 2 · Q29

Application of Derivatives question

2012 · Shift 2 · Q29

JEE AdvancedMathematicsApplication of DerivativesMCQ+4 / −1

Let

f\left( x \right) = {\left( {1 - x} \right)^2}\,\,{\sin ^2}\,\,x + {x^2}

for all

x \in IR

and let

g\left( x \right) = \int\limits_1^x {\left( {{{2\left( {t - 1} \right)} \over {t + 1}} - In\,t} \right)f\left( t \right)dt}

for all

x \in \left( {1,\,\infty } \right)

. Which of the following is true?

A
$g$ is increasing on $\left( {1,\infty } \right)$
B
$g$ is decreasing on $\left( {1,\infty } \right)$
C
$g$ is increasing on $(1, 2)$ and decreasing on $\left( {2,\infty } \right)$
D
$g$ is decreasing on $(1, 2)$ and increasing on $\left( {2,\infty } \right)$

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