If e^ x^2 x^3 d x=e^ x^2 f(x)+C (where C is a constant of integration) and f(1)=0 , then value of f(2) will be

Step-by-step solution

e^ x^2 x^3 = 1 2 x^2 e^ x^2 2 x d x= 1 2 t e^t d t [ let x^2=t ] Integrating by parts aligned & = 1 2 [t e^t-e^t ]+C & = 1 2 [x^2 e^ x^2 -e^ x^2 ]+C=e^ x^2 1 2 (x^2-1 )+C & f(x)= 1 2 (x^2-1 ) f(2)= 3 2 aligned