Question

show that x^3 cosnx is an odd function and x^3sinnx is an even ∫_π^π▒〖x^3 cosnxdx〗someone help please

Answer 1

@phillemon
in case of "cos" function put x=(-x) ,you will get x^3=-x^3& cosnx=cosnx.
so,f(x)=-f(-x),hence x^3cosnx is an "odd" function.
while after putting -x at the place of x, you will get x^3=-x^3 & sinnx=-sinnx.
so you get f(x)=f(-x),hence x^3sinnx is an "even" function