A minimum value of ₀^x t e^ t^2 d t is

Step-by-step solution

We have, ₀^x t e^ t^2 d t Let t^2=z 2 t d t=d zf(x)= ₀^ x^2 e^z 2 d z= 1 2 [e^z ]₀^ x^2 f(x)= 1 2 [e^ x^2 -1 ] On differentiating both sides w.r.t. x , f^ (x)= 1 2 [2 x e^ x^2 ] For maxima or minima, put f^ (x)=0 . x=0f^ (x)=e^ x^2 +2 x e^ x^2 f^ (0)=1>0 f(x) is minimum at x=0 f(0)= 1 2 [e^0-1 ]=0