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Derivative of an integral with parameter

I want to know how to calculate the derivative of this integral, assuming that all our functions are bounded and smouths on some interval of $\mathbb{R}$: $$F(x)=\int_{\phi(x)}^{\psi(x)} f(x,t) dt$$
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stieltjes-integral with sgn(sinx) How integrate?

$\int_{-\pi}^{\pi} (x+2) d(sign\sin x)$ how to calculate the integral Stieltjes? I know what $\int f(x) dg(x) = \int f(x)g(x)'dx$ But derivative sign(sinx)'=0? But then how to decide?
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Exercise 3.22 from W. Lawvere. Sets For Mathematics.

I can't solve Exercise 3.22 from W. Lawvere - Sets For Mathematics book. Exercise 3.22. Show that for any $A$, $1 \times A \simeq A$. The exercise has the following hint. Hint: To show one of ...
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When the sum of two permutations is a permutation?

I have to work with encrypted data, a problem arises as follows: Assume that we have $\sigma_1, \sigma_2 \in S_X$, where we consider the set $X$ as the abelian group $Z_n$. Each element of $X$ is an ...
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If A is path connected then intA is connected - is it true? Explain [on hold]

My views :if A is path connected then intA is also path connected. So intA is connected.
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If $K$ and $F$ are monotone, when is $I+KF$ monotone?

It is known that if $K$ and $F$ are monotone, that $I+KF$ may not be monotone. For example, if $F(x,y)=(x+y, y-x)$ and $K(u,v)=(u+2v, v-2u)$ then $F$ and $K$ are monotone. However, $I+KF$ is not ...
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I am trying to solve cp decomposition for 3 and 4 way tensor. For 3 way tensor: $Y=Q\times _1 A\times _2B\times _3\times C$ For 4 way tensor: $Y=Q\times _1 A\times _2B\times _3\times C\times _4 D$ ...
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What sorts of models are out there for cooperative games with strategic elements?

I want to look at games where there are coalitions as well as individuals who are trying to maximize personal utility. What papers are out there for these sorts of games?
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How can I find the function $f(t,x)$ from the given integral equation?

$$\int_0^\infty f(t, x) = \frac{2}{B+tC}$$ given, initial condition : $f(0,x)=\frac{N_0}{x_0}\exp(-x/x_0)$ here, $N_0,x_0,B,C$ are constants
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