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KCET2014MathematicsParabola

If ( f(x)=f( +e-x) ) and ( _ e ^ I I f(x) d x= 2 e+ ^ ), then ( _ e ^ I I x f(x) d x ) is equal to

Options

  1. A( +e 2 )
  2. B( -e 2 )
  3. CII ( -e )
  4. D( 1 )

Correct answer

D. ( 1 )

Step-by-step solution

Given that [ array l f(x)=f( +e-x) (1) and _ e ^ f(x) d x= 2 e+ (2) array ] Now, [ array l I= _ e ^ x f(x) d x= _ e ^ (e+ -x) f(e+ -x) d x = _ e ^ (e+ -x) f(x) d x= _ e ^ (e+ ) f(x)-I 2 I=(e+ ) 2 e+ I=1 array ]

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