Show that if $\int_{a}^{b}g(t)dt=0$ then $g(t)=0$ for all $t\in[a,b]$
54940
If integral is zero and function is continuous and non negative, then what about the function?
136574
Show $g^{(n)}(0)=0$ for all $n$
34398
Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$
92089
If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$
99458
Suppose $\int_{[a,b]}f=0,\text{ then }f(x)=0 \forall x\in[a,b]$
142025
How can I show that if $f\in L^p(a, b)$ then $\lim_{t\to 0^{+}}\int_{a}^b |f(x+t)-f(x)|^p\ dx=0$..
113141
Prove that $\lim_{n \to \infty}\bigg[\int_0^1f(t)^n \text{dt}\bigg]^{1/n}=M$
142821
Why?$\int_0^1\int_{u(t)}^{u(t)+w(t)} f(t,v(t)) dv dt = \int_0^1 f(t,u(t)+\theta w(t))w(t) dt; ~~\theta\in[0,1] $
116389
If $\exp(t(A + B)) = \exp(tA) \exp(tB)$ for all $t \geq 0$ then $A,B$ commute
81181
Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$
7384
How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
58832
How prove this $\int_{a}^{b}[f''(x)]^2dx\ge\dfrac{4}{b-a}$
33196
show that A(T) is a group under operation of composition of functions
104510
For continuous $f$, $\int_0^x f(t)dt = ∫_x^1f(t)dt$ implies $f=0$.
66404
Prove that:$\int_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) dx$
143608
Show the Trace$(B)^{2} \leq$ nTrace$(B^{T}B)$
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$