MHT CET202415 May 2024Evening ShiftMathematicsIndefinite IntegrationActual
If e ^ x^2 . x^3 ~d x= e ^ x^2 f (x)+ c and f ( I )=0 (where c is a constant of integration), then the value of f (x) is
Options
- Ax-1 2
- Bx^2+1 2
- Cx+1 2
- Dx^2-1 2
Correct answer
D. x^2-1 2
Step-by-step solution
aligned & Let I = e ^ x ^2 x^3 ~d x & Put x^2= t & 2 x ~d x= dt & I= 1 2 e ^ t t dt & = 1 2 (t e^t- 1 e^t ) & = 1 2 ( te ^ t - e ^ t )+ c & = 1 2 e ^ t ( t -1)+ c = 1 2 e ^ x^2 (x^2-1 )+ c & f (x)= x^2-1 2 aligned