If (A_n= _ 2 e^ -x ^n x d x ), then ( A₄-A₆ A₄ = )

Step-by-step solution

We have, ( aligned & A₆= _ 2 ^ e^ -x ^6 x d x & = [-e^ -x ^6 x ]_ 2 ^ - _ 2 ^ (-e^ -x ) 6 ^5 x(- x) d x & =0-6 _ 2 ^ e^ -x ^5 x x d x & A₆ -6 = _ 2 ^ e^ -x ^5 x x d x & -1 6 A₆= [-e^ -x ^5 x x ]_ 2 ^ & - _ 2 ^ (-e^ -x ) [5 ^4 x(- x) x+ ^5 x x ] d x & -1 6 A₆=0+ _ 2 ^ e^ -x [-5 ^4 x (1- ^2 x )+ ^6 x ] d x & -1 6 A₆=-5 _ 2 ^ e^ -x ^4 x d x+6 _ 2 ^ e^ -x ^6 x d x & -1 6 A₆=-5 A₄+6 A₆ & 5 A₄= 37 6 A₆ & A₆= 30 37 A₄ & A₄-A₆ A₄ = A₄- 30 37 A₄ A₄ = 7 37 aligned )