- #1
matteo86bo
- 60
- 0
If I have
[tex]\int_0^{+\infty}h(x)g(x)dx=0
[/tex]
where [tex]h(x)>0[/tex] in [tex][0,+\infty][/tex]. Can I conclude that [tex]g(x)[/tex] might be zero or an odd function in such interval?
If the condition above is still valid and I add this request:
[tex]
g(x)=(f(x)-q)
[/tex]
where [tex]f(x)[/tex] is positive function in the interval. Can I say that [tex]g(x)[/tex] must be zero anywhere?
[tex]\int_0^{+\infty}h(x)g(x)dx=0
[/tex]
where [tex]h(x)>0[/tex] in [tex][0,+\infty][/tex]. Can I conclude that [tex]g(x)[/tex] might be zero or an odd function in such interval?
If the condition above is still valid and I add this request:
[tex]
g(x)=(f(x)-q)
[/tex]
where [tex]f(x)[/tex] is positive function in the interval. Can I say that [tex]g(x)[/tex] must be zero anywhere?