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Tagged with bounds-of-integration indefinite-integrals
3
questions
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votes
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46
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For which lower bound of integration $a$ does a definite integral of $f(x)$ from $a$ to $x$ equal its antiderivative $F(x)$ with $C=0$?
For an arbitrary antidifferentiable function $f(x)$, my goal is to construct a definite integral of $f(x)$:
$$
\int_a^x f(t) dt
$$
which is equal to one of the infinitely-many antiderivatives of $f(x)$...
- 43
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$1/x$ simple integral with different starting conditions
I simply want to test:
$\displaystyle{\int} \dfrac{1}{T_0\,-\Gamma(h-h_0)}\,\mathrm{dh}$ with $T(h_0) = T_0$
is the same as
$\displaystyle{\int_{h_0}^{h}} \dfrac{1}{T_0\,-\Gamma(h-h_0)}\,\mathrm{dh}$
...
- 1,117
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Fixing the bounds of an indefinite integral
Question:
$$\frac{\partial^2 u}{\partial x^2}-\frac{\partial^2 u}{\partial t^2}=f(x,t) \qquad \qquad u(x,0)=\frac{\partial u}{\partial t}(x,0)=0$$
Solve this equation, writing the solution in the ...
- 4,945