AP EAMCET201825 Apr 2018Morning ShiftMathematicsIndefinite IntegrationActual
If x 3 ( 2 x - 1 ) ( x - 1 ) 2 = A + B 2 x - 1 + C x - 1 + D ( x - 1 ) 2 , then 2 A - 3 B + 4 C + 5 D =
Options
- A21 2
- B23 2
- C14
- D19 2
Correct answer
C. 14
Step-by-step solution
We have, x 3 ( 2 x - 1 ) ( x - 1 ) 2 = A + B 2 x - 1 + C x - 1 + D x - 1 2 Now, D r = ( 2 x - 1 ) ( x - 1 ) 2 = ( 2 x - 1 ) ( x 2 - 2 x + 1 ) = 2 x 3 - 5 x 2 + 4 x - 1 Now, x 3 ( 2 x - 1 ) ( x - 1 ) 2 = 1 2 2 x 3 ( 2 x - 1 ) ( x - 1 ) 2 = 1 2 2 x 3 - 5 x 2 + 4 x - 1 + 5 x 2 - 4 x + 1 ( 2 x - 1 ) ( x - 1 ) 2 = 1 2 1 + 5 x 2 - 4 x + 1 ( 2 x - 1 ) ( x - 1 ) 2 = 1 2 + 1 2 5 x 2 - 4 x + 1 ( 2 x - 1 ) ( x - 1 ) 2     . . . i Now, 5 x 2 - 4 x + 1 2 x - 1 x - 1 2 = B 2 x - 1 + C x - 1 + D x - 1 2 ⇒ 5 x 2 -