Question

Integrals (attached)

Answer 1

true or false?
\[\int\limits_{a}^{b} [f(x)g(x)dx] = [\int\limits_{a}^{b} [f(x)]dx][\int\limits_{a}^{b}[g(x)dx]\]
i wanna say true because there's a limit definition of the same kind of thing...

Answer 2

that's false. take f(x) = g(x) =1, a = 0, b = 1/2