- #1

madah12

- 326

- 1

## Homework Statement

show that

xf(x)=integral from 0 to infinity of [B*(w)sin(wx)]dw , // B* is a function not B * w

where B* = -dA/dw

A(w) = 2/pi integral from 0 to infinity [f(v) cos(wv)] dv

## Homework Equations

f(x)=integral from 0 to infinity [A(w)cos(wx)] dw

## The Attempt at a Solution

working on right hand side

B*= 2/pi * integral from 0 to infinity [vf(v)cos(wv)dv]

=integral from 0 to infinity of [2/pi * integral from 0 to infinity [vf(v)cos(wv)dv]sin(wx)]dw

left side = integral from 0 to infinity [ A(w)xcos(wx)]dw

Even when i tried writing A as integral i dont see how do i prove 2 sides which have 2 integrals in them equal each other?