MHT CET202019 Oct 2020Morning ShiftMathematicsIndefinite IntegrationActual
x²+1 (x-3)(x-2) d x=P x+Q |x-3|+R |x-2|+c , where c is constant of integration, then the values of P , Q , R are, respectively
Options
- A0,10,5
- B0,10,-5
- C1,10,5
- D1,10,-5
Correct answer
D. 1,10,-5
Step-by-step solution
(C) I= x²+1 (x-3)(x-2) d x= (x²-5 x+6 )+(5 x-5) (x-3)(x-2) d x = x²-5 x+6 x²-5 x+6 d x+5 x-1 (x-3)(x-2) d x Let (x-1) (x-3)(x-2) = A (x-3) + B (x-2) (x-1)=A(x-2)+B(x-3) A+B=1 and 2 A+3 B=1 A=2, B=-1 I= d x+5 [ 2 (x-3) - 1 (x-2) ] d x Thus P=1, Q=10, R=-5