Question

True or False

Answer 1

\[If \int\limits_{0}^{1}f(x)dx=0, then f(x)=0 For All 0<x<1\]

Answer 2

Observe that \[\int\limits_{0}^{1}f(x)dx = F(1)-F(0)\]

Think, is there any possible counter-example that you could provided to disprove the statement?

Note,
\[\int\limits_{0}^{1}(2x-3x^2)dx = F(1) -F(0)= 0\]

So, the statement is false.

Answer 3

Wait. I misread.

Answer 4

The statement is still false, however.

Imagine if A1 = A2. Then the statement is false.