The value of _ x 0 e^ a x -e^ b x 2 x is equal to

Step-by-step solution

aligned & _ x 0 e^ a x -e^ b x 2 x & = _ x 0 (1+a x+ (a x)^2 2 ! + (a x)^3 3 ! + ) - (1+b x+ (b x)^2 2 ! + (b x)^3 3 ! ) & = _ x 0 [ array c .(a-b)+ ( a^2 x 2 x + a^3 x^2 3 ! + ) ] .+ ( b^2 x 2 ! + b^3 x^2 3 ! + ) ] 2 x array ] [ array c 3 ! 2 x array ] aligned aligned & = 1 2 [(a-b)+(0+0+ )+(0+0+ )] & = a-b 2 aligned