- #1
YoungEverest
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Note: This is not a homework problem but merely independent study, if it's in the wrong place, please move!
I want to know how changing a square integrable function changes the result of an integral. So that if a function is square integrable and you multiply it by x, is it still square integrable?
If [tex]\int[/tex] |f(x)|^2 dx < [tex]\infty[/tex]
then is [tex]\int[/tex] x^2 |f(x)|^2 dx < [tex]\infty[/tex] ?
I have no idea how to attempt this, I just have a feeling that it is true as multiplying by x should not change the fact that the area under the curve is contained, and not open at +/- infinity.
Homework Statement
I want to know how changing a square integrable function changes the result of an integral. So that if a function is square integrable and you multiply it by x, is it still square integrable?
Homework Equations
If [tex]\int[/tex] |f(x)|^2 dx < [tex]\infty[/tex]
then is [tex]\int[/tex] x^2 |f(x)|^2 dx < [tex]\infty[/tex] ?
The Attempt at a Solution
I have no idea how to attempt this, I just have a feeling that it is true as multiplying by x should not change the fact that the area under the curve is contained, and not open at +/- infinity.