Question

\[\int_0^1 t x(t) y(t) dt\] please help

Answer 1

I am supposed to do it by part but not sure how

Answer 2

Do you know what the form of the final answer is? Is it one of those "Show that __ gives "answer" " questions?

Answer 3

Or is there any information about the functions \(x(t)\) and \(y(t)\)?

Answer 4

@kirbykirby actually, it is a part of the problem. I need to define a linear transformation is self-adjoint or not. By definition of self-adjoint transformation in inner product space which defined by (x,y) =\(\int_0^1 x(t)\bar y(t) dt\)
and (Tx)(t) = t*x(t)
Following the definition, I construct (Tx(t), y(t) )= (x(t) , T^(start)y(t) )
That process needs taking that integral

Answer 5

I got it, thanks for reply any way, hihihihihihihi:):):)

Answer 6

oh great then :)