Why does $\int_a^b fg\, dx = 0$ imply that $f = 0$?
72660
How can I show that $f$ must be zero if $\int fg$ is always zero?
15908
Is it true that $\int_{a}^b h^2=0\implies h=0$?
105569
If $f$ is integrable in $[a-1,b+1]$, then prove that $\lim \limits_{h\to 0} \ \int_{a}^{b}|f(x+h)-f(x)| ~ dx=0$
143874
Limit of derivative is zero. Does it imply a limit for f(x)?
95260
Let $m$ be Lebesgue measure and $a \in R$. Suppose that $f : R \to R$ is integrable, and $\int_a^xf(y) \, dy = 0$ for all $x$. Then $f = 0$ a.e.
137664
What exactly is $F$ in $W = \int_{a}^{b} F dx$?
136966
Riemann integral proof $\int^b_a f(x) \, dx>0$
158335
Why is this $0 = 1$ proof wrong?
142025
How can I show that if $f\in L^p(a, b)$ then $\lim_{t\to 0^{+}}\int_{a}^b |f(x+t)-f(x)|^p\ dx=0$..
66451
In a ring, how do we prove that a * 0 = 0?
18261
Prove $\int_{a}^{b}{f(x)dx}>0$.
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
95469
Suppose $f:[0,1] \Rightarrow \mathbb{R}$ is continuous and $\int_0^x f(x)dx = \int_x^1 f(x)dx$. Prove that $f(x) = 0$ for all $x$
48563
If $\Gamma^k_{ij}(p)=0$, then $\nabla_{E_i}E_j (p)=0?$
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
42853
If $f \geq 0$ is continuous and $\int_{a}^{b} f(x) \, dx = 0$, then $f =0$
4656
Prove that there is a $\delta$ such that $\int_{0}^{1} (f(x))^2dx\leq \delta$$\int_{0}^{1} (f'(x))^2dx$ for all $f$ with these conditions