MHT CET202411 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
x ~d x (x-1)^2(x+2) =
Options
- A2 9 (x-1)+ 1 3 1 x-1 + 2 9 (x+2)+ c , where c is a constant of integration
- B2 9 (x-1)- 1 3 1 (x-1) + 2 9 (x+2)+ c , where c is a constant of integration
- C2 9 (x-1)+ 1 3 1 x-1 - 2 9 (x+2)+ c , where c is a constant of integration
- D2 9 (x-1)- 1 3 1 x-1 - 2 9 (x+2)+ c , where c is a constant of integration
Correct answer
D. 2 9 (x-1)- 1 3 1 x-1 - 2 9 (x+2)+ c , where c is a constant of integration
Step-by-step solution
Let I= x (x-1)^2(x+2) d x Let x (x-1)^2(x+2) = A (x-1) + B (x-1)^2 + C (x+2) x= A (x-1)(x+2)+ B (x+2)+ C (x-1)^2 for x=1 , we get B = 1 3 for x=-2 , we get C = -2 9 Equating the coefficients of x^2 , we get A + C =0 A= 2 9 aligned I & = 2 9 1 (x-1) d x+ 1 3 1 (x-1)^2 ~d x- 2 9 1 (x+2) d x & = 2 9 (x-1)- 1 3 1 (x-1) - 2 9 (x+2)+ c aligned