KCET2019MathematicsIndefinite Integration
( 2 x-1 (x-1)(x+2)(x-3) d x=A |x-1|+B |x+2|+C |x-3|+K ), then ( A, B ), C are respectively
Options
- A( 1 6 , 1 3 , 1 5 )
- B( -1 6 , -1 3 , 1 2 )
- C( -1 6 , 1 3 , -1 2 )
- D( 1 6 , -1 3 , 1 3 )
Correct answer
B. ( -1 6 , -1 3 , 1 2 )
Step-by-step solution
(B) ( 2 x-1 (x-1)(x+2)(x-3) d x=A |x-1|+B |x+2|+C |x-3|+K ) Diff w.r.t ' ( x ) ' ( 2 x-1 (x-1)(x+2)(x-3) = A (x-1) + B (x+2) + C (x-3) ) ( 2 x-1=A(x+2)(x-3)+B(x-1)(x-3)+C(x-1)(x+2) ) Comparing constants ( -1=-6 A+3 B-2 C ) ( A= -1 6 , B= -1 3 , C= 1 2 )