MHT CET202611 April 2026Evening ShiftMathematicsIndefinite IntegrationActual
2x 4 - 3x - x^2 dx =
Options
- A8 5 |4 + x| - 2 5 |1 - x| + c
- B2 |4 + x| + 2 5 |1 - x| + c
- C- |4 + x| + 2 5 |1 - x| + c
- D- 8 5 |4 + x| - 2 5 |1 - x| + c
Correct answer
D. - 8 5 |4 + x| - 2 5 |1 - x| + c
Step-by-step solution
Let I = 2x 4 - 3x - x^2 dx Factorizing the denominator: 4 - 3x - x^2 = (1 - x)(4 + x) Using partial fractions: 2x (1 - x)(4 + x) = A 1 - x + B 4 + x 2x = A(4 + x) + B(1 - x) Substituting x = 1 , we get 2 = 5A A = 2 5 Substituting x = -4 , we get -8 = 5B B = - 8 5 Therefore, I = ( 2/5 1 - x - 8/5 4 + x ) dx I = 2 5 ( |1 - x| -1 ) - 8 5 |4 + x| + c I = - 8 5 |4 + x| - 2 5 |1 - x| + c Answer: - 8 5 |4 + x| - 2 5 |1 - x| + c