MHT CET20242 May 2024Evening ShiftMathematicsIndefinite IntegrationActual
x 3 x ~d x is equal to
Options
- A1 3 ( x )+ c , (where c is a constant of integration)
- B2 3 ( x )^2+ c , (where c is a constant of integration)
- C2 3 ( x)^2+ c , (where c is a constant of integration)
- D1 12 ( x)^2+ c ,( where c is a constant of integration)
Correct answer
D. 1 12 ( x)^2+ c ,( where c is a constant of integration)
Step-by-step solution
aligned & Put x= t ^2 ~d x=2 tdt & aligned x 3 x ~d x & = t 3 t ^2 (2 tdt ) & = 2 3 t t dt & = 2 3 ( t )^2 2 + c = ( x )^2 3 + c & = 1 3 ( 1 2 x )^2+ c & = 1 12 ( x)^2+ c aligned aligned