If I= _ -a ^a (x^4-2 x^2 ) d x , then I is minimum at a=

Step-by-step solution

aligned & I= _ -a ^a (x^4-2 x^2 ) d x & d I d a = d d a [ _ -a ^a (x^4-2 x^2 ) d x ] & =2 a^4-4 a^2 & and d^2 I d a^2 =8 a^3-8 a aligned For minima, d I d =0 a=0, 2 but when c= 2 then d^2 I d a^2 =8 2 >0 Hence a= 2 is minima