Consider the function f : (- ∞ , ∞) → (- ∞ , ∞) defined by f (x) = \frac{x^2-ax+1}{x^2+ax+1} , 0 < a < 2. Let g (x) = \int^{e^x}_{0} \frac{f'(t)}{1+t^2} dt , which of the following is true? [JEE Adv 2008 P2]

Correct Answer is : g′(x) is negative on (−∞, 0) and positive on (0, ∞).

g′(x) is positive on (−∞, 0) and negative on (0, ∞).

g′(x) is negative on (−∞, 0) and positive on (0, ∞).

g′(x) changes sign on both (−∞, 0) and (0, ∞).

g′(x) does not change sign on (−∞, ∞).

Definite Integration

Section: Mathematics

Question : 45 of 46

Marks: +1, -0

Consider the function
f : (- ∞ , ∞) → (- ∞ , ∞) defined by f (x) =

x2−ax+1

x2+ax+1

, 0 < a < 2.
Let g (x) =

∫

f′(t)

1+t2

dt , which of the following is true?

[JEE Adv 2008 P2]

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