MHT CET202523 Apr 2025Evening ShiftMathematicsIndefinite IntegrationActual
(5 -2) (5- ^2 -4 ) d =
Options
- A(5 -2)+c , where c is the constant of integration
- B5 ( -2)- 8 ( -2) +c , where c is the constant of integration
- C(5 -2)+ 8 ( -2) +c, where c is the constant of integration
- D(5 -2)+ 1 ( -2) +c, where c is the constant of integration
Correct answer
B. 5 ( -2)- 8 ( -2) +c , where c is the constant of integration
Step-by-step solution
Substitute t = , so dt = d . Using ^2 = 1 - t^2 , the integral becomes I = 5t - 2 t^2 - 4t + 4 dt . The denominator simplifies as (t-2)^2 . Let u = t - 2 , so t = u + 2 and dt = du . The integral becomes I = 5u + 8 u^2 du = 5 |u| - 8 u + C . Substitute back u = t - 2 and t = to obtain I = 5 | - 2| - 8 - 2 + C . Since - 2 I = 5 (2 - ) - 8 - 2 + C . Final answer: B