If a=2 n and b=2 m+1 for all m, n N , _ - ^ e^ ^a x ^b(2 n+1) x d x=

Step-by-step solution

Given a=2 n, b=2 m+1 and m, n N Let I= _ - ^ e^ ^a x ^b(2 n+1) x d x Let f(x)=e^ ^a x ^b(2 n+1) x f(-x)=e^ ^a(-x) ^b(2 n+1)(-x) Since a is even number and b is odd number and (- )=- aligned & f(-x)=e^ ^a(x) [- ^b(2 n+1) x ] d x & f(-x)=-f(x) aligned Hence I= _ - ^ f(x) d x=0 array l f(-x)=-f(x) _ -a ^a f(x) d x=0 array .