Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
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

  1. A( 1 6 , 1 3 , 1 5 )
  2. B( -1 6 , -1 3 , 1 2 )
  3. C( -1 6 , 1 3 , -1 2 )
  4. 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 )

Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

If 5 x x -2 dx = ax + b | x -2 x |+ c , then a + b = 2025x Cos ⁻¹ ( 1-x^2 1+x^2 ) d x(x>0)= 2025d x (1+ x ) x-x^2 = 2025If x x x+1 ~d x= f (x)+ k , then f ( 4 )= 2025If x^4+1 x^2+1 d x=A x^3+B x^2+C x+D Tan ⁻¹ x+E , then A+B+C+D= 2025If x^2-x+2 x^2+x+2 d x=x- (f(x))+ 2 7 Tan ⁻¹(g(x))+c , then f (-1)+ 7 ~g (-1)= 2025(x- 3 ) (x+ 6 ) d x= 2025If a x+3 x 5 x+2 x d x= 26 29 x- k 29 |5 x+2 x|+c , then |a+k|= 2025 Full Indefinite Integration list All KCET PYQs