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Let g : (0, ∞ ) → R be a differentiable function such that ∫ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − + + + − 2 x x x x ) 1 e ( ) xe 1 e )( x ( g 1 e ) x sin x (cos x dx = 1 e ) x ( xg x + + c, for all x > 0. where c is and arbitrary constant. then :

1. g is decreasing in ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π 4 , 0
2. g ′ is increasing in ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π 4 , 0
3. g + g ′ is increasing in ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π 2 , 0
4. g – g ′ is increasing in ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π 2 , 0

Correct answer: g – g ′ is increasing in ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π 2 , 0

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