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99 Percentile Qs Bank for JEE MainMathematicsDefinite Integration

If g(x)= ₀^x ^4 t ~d t , then g(x+ ) equals

Options

  1. Ag(x)+g( )
  2. Bg(x)-g( )
  3. Cg(x) g( )
  4. Dg(x) g( )

Correct answer

A. g(x)+g( )

Step-by-step solution

aligned & g(x)= ₀^x ^4 t ~d t & g(x+ )= ₀^ x+ ^4 t ~d t= ₀^x ^4 t ~d t+ _x^ x+ ^4 t ~d t & =g(x)+ _x^ x+ ^4 t ~d t & =g(x)+ ₀^ ^4 t ~d t aligned [as ^4 t is a periodic function with period . ]=g(x)+g( )

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