Show using an example 𝑓 and 𝑔 are not integrable on [𝑎, 𝑏], but 𝑓𝑔 may be integrable on [𝑎, 𝑏].
f(x)="\\{\\begin{matrix}\n 1,if x\\epsilon [0,1]\\\\\n 0,elsewhere\n\\end{matrix}"
g(x)="\\{\\begin{matrix}\n 0,if x\\epsilon [0,1]\\\\\n 1,elsewhere\n\\end{matrix}"
f.g=0
Here, f and g are not integrable but f.g is integrable( since constant function).
Comments
Leave a comment