Question

Confused about variable substitution

Answer 1

If such equation holds:
\[\int\limits\limits_{0}^{1}f(x)g(x)xdx=0\]
will this hold:
\[x=t^{2}\]
\[\int\limits\limits_{0}^{1}f(t ^{2})g(t ^{2}) 2t ^{3} dt=0\]
Thank you.

Answer 2

Only if the f(x)=g(x)=t^2

Answer 3

f(x) and g(x) are polynomials with variable x, could you explain a bit more about it?

Answer 4

Well then, in that case, it would be true.