MHT CET20228 Aug 2022Evening ShiftMathematicsDefinite IntegrationActual
If g(x)= ₀^x ^4 t ~d t , then g(x+ ) equals
Options
- Ag(x)+g( )
- Bg(x)-g( )
- Cg(x) g( )
- 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( )