MHT CET202611 April 2026Evening ShiftMathematicsIndefinite IntegrationActual
The value of 1 x^2 - 5x + 8 dx is equal to...
Options
- A2 7 ⁻¹ ( 2x+5 7 ) + c
- B- 2 7 ⁻¹ ( 2x-5 7 ) + c
- C2 7 ⁻¹ ( 2x-5 7 ) + c
- D- 2 7 ⁻¹ ( 2x+5 7 ) + c
Correct answer
C. 2 7 ⁻¹ ( 2x-5 7 ) + c
Step-by-step solution
Let I = 1 x^2 - 5x + 8 dx Completing the square in the denominator: x^2 - 5x + 8 = x^2 - 5x + 25 4 - 25 4 + 8 = (x - 5 2 )^2 + 7 4 Substituting this into the integral: I = 1 (x - 5 2 )^2 + ( 7 2 )^2 dx Using the standard formula 1 X^2 + a^2 dX = 1 a ⁻¹ ( X a ) + c : I = 1 7 2 ⁻¹ ( x - 5 2 7 2 ) + c I = 2 7 ⁻¹ ( 2x - 5 7 ) + c Answer: 2 7 ⁻¹ ( 2x-5 7 ) + c