enfield
Dec10-11, 01:58 AM
Why don't integrals such as ∫_{0}^{1}sin(πx)sin(3πx) = 0 violate the lemma? both functions are continuous and equal to zero at the boundaries of the integral, but neither is equal to zero over the whole interval. I'm scared that I haven't been able to figure this out.
Nevermind =P. I didn't understand that if ∫_{a}^{b}f(x)g(x) = 0 then one can only conclude f(x) = 0 if it is true that *for all* functions g(x), g(a) = g(b) = 0.
Nevermind =P. I didn't understand that if ∫_{a}^{b}f(x)g(x) = 0 then one can only conclude f(x) = 0 if it is true that *for all* functions g(x), g(a) = g(b) = 0.