If 1 a ^2 ^2 x+ b ^2 ^2 x ~d x= 1 12 ⁻¹(3 x)+ constant, then the maximum value of a x+ b x , is :

Step-by-step solution

aligned & ^2 x d x a^2 ^2 x+b^2 & let x=t & ^2 d x=d t & d t a^2 t^2+b^2 & 1 a^2 d t t^2+ ( b a )^2 & 1 a^2 1 b a ⁻¹ ( t b a )+c & 1 a b ⁻¹ ( b x )+c aligned on comparing a b =3 aligned & a b=12 & a=6, b=2 aligned maximum value of 6 x+2 x is 40