If f (x)= array ll e ^ x x & , for |x| 2 2, & otherwise array . , then _ -2 ^3 f (x) d x is equal to

Step-by-step solution

aligned _ -2 ^3 f (x) d x & = _ -2 ^2 f (x) d x+ ₂^3 f (x) d x & = _ -2 ^2 e ^ x x ~d x+ ₂^3 2 ~d x aligned Since e ^ x x is an odd function. _ -2 ^3 f (x) d x=0+2(3-2)=2