AP EAMCET202423 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
If x x ^4 x- ^4 x d x=- f(x) 2 +c , then domain of f(x) is
Options
- A[2 n (2 n+1) ] n=0,1,2
- B[(4 n-1) 2 ,(4 n+1) 2 ], n=0,1,2,
- C[(4 n-1) 4 ,(4 n+1) 4 ], n=0,1,2,
- D[ (2 n 4 ,(2 n+1) 4 ], n=0,1,2, .
Correct answer
C. [(4 n-1) 4 ,(4 n+1) 4 ], n=0,1,2,
Step-by-step solution
I= x x ^4 x- ^4 x d x I= 1 2 2 x 2 x d x Let 2 x=t -2 2 x d x=d t I= -1 4 1 t d t I= -1 2 t +C I= - 2 x 2 +C On comparing with -f(x) 2 +C f(x)= 2 x For domain : 2 x 0 (2 n- 1 2 ) 2 x (2 n+ 1 2 ) (4 n-1) 4 x (4 n+1) 2 , n=0,1,2, . .